diff --git a/lib/source-map-consumer.js b/lib/source-map-consumer.js
index db0a5324..ee661146 100644
--- a/lib/source-map-consumer.js
+++ b/lib/source-map-consumer.js
@@ -151,7 +151,9 @@ SourceMapConsumer.prototype.eachMapping =
     for (var i = 0, n = mappings.length; i < n; i++) {
       var mapping = mappings[i];
       var source = mapping.source === null ? null : sources.at(mapping.source);
-      source = util.computeSourceURL(sourceRoot, source, sourceMapURL);
+      if(source !== null) {
+        source = util.computeSourceURL(sourceRoot, source, sourceMapURL);
+      }
       boundCallback({
         source: source,
         generatedLine: mapping.generatedLine,
@@ -1142,7 +1144,9 @@ IndexedSourceMapConsumer.prototype._parseMappings =
         var mapping = sectionMappings[j];
 
         var source = section.consumer._sources.at(mapping.source);
-        source = util.computeSourceURL(section.consumer.sourceRoot, source, this._sourceMapURL);
+        if(source !== null) {
+          source = util.computeSourceURL(section.consumer.sourceRoot, source, this._sourceMapURL);
+        }
         this._sources.add(source);
         source = this._sources.indexOf(source);
 
diff --git a/test/test-source-map-generator.js b/test/test-source-map-generator.js
index b930515c..fae7d4a1 100644
--- a/test/test-source-map-generator.js
+++ b/test/test-source-map-generator.js
@@ -768,3 +768,18 @@ exports['test numeric names #231'] = function (assert) {
   assert.equal(map.names.length, 1, "Should have one name");
   assert.equal(map.names[0], "8", "Should have the right name");
 };
+
+exports['test that we can create a generator from a source map with empty mappings'] = function (assert) {
+  var generator = new SourceMapGenerator();
+  generator.addMapping({
+    generated: { line: 1, column: 1 },
+    original: null,
+    source: null,
+  });
+  const originalMap = generator.toJSON();
+  const consumer = new SourceMapConsumer(originalMap);
+  const fromConsumer = SourceMapGenerator.fromSourceMap(consumer);
+  const fromSourceMap = fromConsumer.toJSON();
+  assert.ok(fromSourceMap, "Creating a generator from a map with only generated position did not throw");
+  assert.equal(fromSourceMap.mappings, originalMap.mappings);
+}
\ No newline at end of file