  In this paper, we first introduce the notion of controlled weaving K-g-frames
in Hilbert spaces. Then, we present sufficient conditions for controlled
weaving K-g-frames in separable Hilbert spaces. Also, a characterization of
controlled weaving K-g-frames is given in terms of an operator. Finally, we
show that if bounds of frames associated with atomic spaces are positively
confined, then controlled K-g-woven frames gives ordinary weaving K-frames and
vice-versa.
