A continuous variable valve lift device includes a valve, which opens/closes a channel by means of reciprocation, a control shaft, which is mounted so as to be able to move toward or away from a reciprocation central axis of the valve, a pivotable shoe, which is pivotably coupled to the control shaft, includes a cam insertion part in a recess or through-hole shape and a slide face slidably contacting an end of the valve, and reciprocates the valve when pivoted, and a drive cam, which comes into contact with an inner wall of the cam insertion part, and pivots the pivotable shoe. Thereby, the continuous variable valve lift device can freely adjust a lift amount and a lift time of the valve without changing positions of the drive cam and camshaft, and thus be easily applied to an existing engine.