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 a position thereof is rotatable around a pivot shaft, a control portion configured to selectively push the slider housing to be rotated, a spring guide connected to the slider housing for elastically supporting the slider housing, a rotation deliverer configured to transmit rotation of the camshaft to the cam portion, an output portion rotatable around the pivot shaft and onto which a valve shoe is formed, and a valve unit configured to be driven by the valve shoe.