A continuously variable valve lift apparatus includes an input cam disposed to a camshaft and rotating, a follower supporting portion rotatably disposed to the camshaft for changing a relative angle of the follower with respect to the camshaft, a follower that includes a center shaft, is connected with the follower supporting portion via the center shaft, and pivots around the center shaft by receiving rotation movement of the input cam, a straight line guide, an output cam that contacts the follower and reciprocates along the straight line guide, and a valve opening unit that is opened by pushing of the output cam.