A continuously variable valve lift apparatus may include a camshaft, a cam portion on which a cam is formed and into which the camshaft is inserted, a slider housing into which the cam portion is rotatably inserted and of which a position is rotatable around a pivot shaft, a control portion engaged with the slider housing and configured to selectively rotate the slider housing around the pivot shaft, an output portion rotatable around the pivot shaft, contacting the cam and onto which a valve shoe is formed, and a valve device contacting the valve shoe and driven by rotation of the cam.