This work deals with admissibilization for degenerate jump systems (DJSs) with distributed delay and discrete state delay. Firstly, admissibility is analysed for the DJSs based on singular value decomposition (SVD) technique and Lyapunov stability theory. Secondly, mode-dependent state feedback controller is designed to actualize admissibilization of the DJSs. L-K functional with delay and MJ modes information is chosen, admissibilization conditions are expressed via linear matrix inequalities (LMIs). A simulation example is employed to certify the validity of the admissibilization method.