diff --git a/README.md b/README.md
index 4e20dd9c..6c135870 100644
--- a/README.md
+++ b/README.md
@@ -308,6 +308,7 @@ Error object:
 * message:
   * 'invalid token' - the header or payload could not be parsed
   * 'jwt malformed' - the token does not have three components (delimited by a `.`)
+  * 'unsupported "crit" header parameter' - the token marks header parameters as critical ([RFC 7515 Section 4.1.11](https://datatracker.ietf.org/doc/html/rfc7515#section-4.1.11)), which this library does not implement
   * 'jwt signature is required'
   * 'invalid signature'
   * 'jwt audience invalid. expected: [OPTIONS AUDIENCE]'
diff --git a/test/header-crit.test.js b/test/header-crit.test.js
new file mode 100644
index 00000000..a67b1ed7
--- /dev/null
+++ b/test/header-crit.test.js
@@ -0,0 +1,85 @@
+'use strict';
+
+const jwt = require('../');
+const expect = require('chai').expect;
+const util = require('util');
+const testUtils = require('./test-utils');
+
+function signWithCrit(crit, extraHeader) {
+  const header = Object.assign({}, extraHeader);
+  if (crit !== undefined) {
+    header.crit = crit;
+  }
+  return jwt.sign({sub: 'foo'}, 'secret', {algorithm: 'HS256', header});
+}
+
+describe('crit', function () {
+  describe('`jwt.verify` with a "crit" header parameter', function () {
+    [
+      // an extension nobody implements
+      ['http://example.invalid/UNDEFINED'],
+      // RFC 7797 unencoded payload: a conformant verifier reads a different payload
+      ['b64'],
+      // names the producer is not even allowed to mark critical
+      ['alg'],
+      // shapes RFC 7515 forbids producers from emitting
+      [],
+      'b64',
+      1,
+      null,
+      {},
+    ].forEach((crit) => {
+      it(`should error with value ${util.inspect(crit)}`, function (done) {
+        const token = signWithCrit(crit, {'http://example.invalid/UNDEFINED': true, b64: false});
+        testUtils.verifyJWTHelper(token, 'secret', {}, (err) => {
+          testUtils.asyncCheck(done, () => {
+            expect(err).to.be.instanceOf(jwt.JsonWebTokenError);
+            expect(err).to.have.property('message', 'unsupported "crit" header parameter');
+          });
+        });
+      });
+    });
+
+    it('should error before the "complete" option can expose the payload', function (done) {
+      const token = signWithCrit(['http://example.invalid/UNDEFINED']);
+      testUtils.verifyJWTHelper(token, 'secret', {complete: true}, (err, decoded) => {
+        testUtils.asyncCheck(done, () => {
+          expect(err).to.be.instanceOf(jwt.JsonWebTokenError);
+          expect(err).to.have.property('message', 'unsupported "crit" header parameter');
+          expect(decoded).to.be.undefined;
+        });
+      });
+    });
+  });
+
+  describe('`jwt.verify` without a "crit" header parameter', function () {
+    it('should verify a token that has no "crit" header', function (done) {
+      const token = signWithCrit(undefined);
+      testUtils.verifyJWTHelper(token, 'secret', {}, (err, decoded) => {
+        testUtils.asyncCheck(done, () => {
+          expect(err).to.be.null;
+          expect(decoded).to.have.property('sub', 'foo');
+        });
+      });
+    });
+
+    it('should verify a token with unrecognized headers that are not marked critical', function (done) {
+      const token = signWithCrit(undefined, {'http://example.invalid/UNDEFINED': true});
+      testUtils.verifyJWTHelper(token, 'secret', {}, (err, decoded) => {
+        testUtils.asyncCheck(done, () => {
+          expect(err).to.be.null;
+          expect(decoded).to.have.property('sub', 'foo');
+        });
+      });
+    });
+  });
+
+  describe('`jwt.decode`', function () {
+    it('should still decode a token with a "crit" header, as it does not verify', function () {
+      const token = signWithCrit(['http://example.invalid/UNDEFINED']);
+      const decoded = jwt.decode(token, {complete: true});
+      expect(decoded.header).to.have.deep.property('crit', ['http://example.invalid/UNDEFINED']);
+      expect(decoded.payload).to.have.property('sub', 'foo');
+    });
+  });
+});
diff --git a/verify.js b/verify.js
index cdbfdc45..50ca8fab 100644
--- a/verify.js
+++ b/verify.js
@@ -83,6 +83,14 @@ module.exports = function (jwtString, secretOrPublicKey, options, callback) {
   }
 
   const header = decodedToken.header;
+
+  //RFC 7515 Section 4.1.11: "crit" lists extension header parameters that must be
+  //understood and processed, and the JWS is invalid if any of them are not. This
+  //library implements no such extension, so any "crit" header is unsupported.
+  if (typeof header.crit !== 'undefined') {
+    return done(new JsonWebTokenError('unsupported "crit" header parameter'));
+  }
+
   let getSecret;
 
   if(typeof secretOrPublicKey === 'function') {