Continuous varible vavle lift apparatus and engine provided with the same

The present invention relates to a continuous variable valve lift device capable of varying a lift of a valve. According to the present invention, the continuous variable valve lift device includes: a cam shaft; a cam unit having a cam, wherein the cam shaft is inserted into the cam unit; a slider housing moving a relative position on the cam shaft of the cam unit by moving the position of the slider housing and having a guide slot, wherein the cam unit is inserted into the slider housing to rotate; a control unit selectively moving the position of the slider housing; a guide shaft guiding a movement of the slider housing by being inserted into the guide slot, wherein the guide shaft is installed to be parallel with the cam shaft; an output unit rotating around a pivot shaft and having a valve shoe; and a valve opening and closing unit opened and closed by being in contact with the valve shoe.