A continuously variable valve lift apparatus may include a camshaft, a cam portion of which a cam is formed thereto and the camshaft is inserted into therein, a slider housing of which the cam portion is rotatably inserted therein, of which a position with respect to the camshaft is movable and of which a guide slot is formed thereto, a control portion selectively changing the position of the slider housing, a guide shaft disposed parallel to the camshaft and inserted into the guide slot for guiding movement of the slider housing, an output portion rotatable around a pivot shaft and of which a valve shoe is formed thereto and a valve unit driven by the valve shoe.