In this paper, we study the excess of continuous $K$-$g$-frames and give some results about this notion.Also, we extend the concept of atomic system to continuous version and study its relations by continuous $K$-$g$-frames. Indeed, we give some equivalent characterizations for continuous $K$-$g$-frames. As well as, the relationship of a continuous $K$-$g$-frame and the range of operator $K$ will be verified. Finally, we study the induced $cK$-frames by continuous $K$-$g$-frames.