A continuous variable valve lift apparatus according to an exemplary embodiment of the present invention includes an input cam disposed to an input shaft, a first shaft in parallel with the input shaft, a first link connected with the first shaft, a second link rotatably connected to the first link, an output cam that is rotatably connected with the second link and configured with a contact portion contacting the input cam, a second shaft disposed to the output cam parallel with the input shaft, at least one valve unit that is opened and closed by the output cam, and a control part that controls a position of the second shaft.