A continuous variable valve lift apparatus according to an exemplary embodiment of the present invention includes a camshaft, an input cam disposed to the camshaft, a variable lever that is rotably connected to the camshaft and includes a first arm including a first connecting shaft and a second arm including a second connecting shaft, a first link rotating around the first connecting shaft corresponding to a rotation of the input cam, an output cam rotating around the camshaft, a valve opening/closing portion that is opened and closed corresponding to a rotation of the output cam, and a connecting portion that is disposed for the output cam to rotate corresponding to a rotation of the first link.