In this paper, we intend to introduce the concept of c-K-g-frames, which are the generalization ofK-g-frames. In addition, we prove some new results on c-K-g-frames in Hilbert spaces. Moreover, we define the related operators of c-K-g-frames. Then, we give necessary and sufficient conditions on c-K-g-frames to characterize them. Finally, we verify the perturbation of c-K-g-frames.
