diff --git a/src/contains.js b/src/contains.js
index 952a62d..ab76bf8 100644
--- a/src/contains.js
+++ b/src/contains.js
@@ -58,13 +58,19 @@ function containsPoint(coordinates, point) {
   return distance(coordinates, point) === 0;
 }
 
-function containsLine(coordinates, point) {
-  var ab = distance(coordinates[0], coordinates[1]),
-      ao = distance(coordinates[0], point),
-      ob = distance(point, coordinates[1]);
+function containsLineSegment(a, b, point) {
+  var ab = distance(a, b),
+      ao = distance(a, point),
+      ob = distance(point, b);
   return ao + ob <= ab + epsilon;
 }
 
+function containsLine(coordinates, point) {
+  var i = -1, n = coordinates.length-1;
+  while (++i < n) if (containsLineSegment(coordinates[i], coordinates[i+1], point)) return true;
+  return false;
+}
+
 function containsPolygon(coordinates, point) {
   return !!polygonContains(coordinates.map(ringRadians), pointRadians(point));
 }
diff --git a/test/contains-test.js b/test/contains-test.js
index 94f7c53..525408b 100644
--- a/test/contains-test.js
+++ b/test/contains-test.js
@@ -113,3 +113,12 @@ tape("null contains nothing", function(test) {
   test.equal(d3.geoContains(null, [0, 0]), false);
   test.end();
 });
+
+tape("a LineString with 2+ points contains those points", function(test) {
+  var points = [[0, 0], [1,2], [3, 4], [5, 6]];
+  var feature = {type: "LineString", coordinates: points};
+  points.forEach(point => {
+    test.equal(d3.geoContains(feature, point), true);
+  });
+  test.end();
+});