A multiple variable valve lift apparatus disposed at an intake part and an exhaust part of an engine includes: a moving cam rotating together with a camshaft, being movably disposed in an axial direction of the camshaft, and forming a plurality of cams for realizing valve lift to be different from each other and a cam guide protrusion; an operating unit selectively guiding the cam guide protrusion so as to move the moving cam in an axial direction of the camshaft; a controller controlling an operation of the operating unit; and a valve opening/closing unit opened/closed by contacting any one among the plurality of cams.