In order to study the finite-time guaranteed cost control problem for impulsive stochastic Markov jump systems with time-varying delays. By selecting mode-dependent Lyapunov functionals, using techniques such as linear matrix inequality (LMI) and average dwell time method, some new sufficient conditions are obtained to ensure finite-time stability of the system, and the upper bound performance index of the system is given. Based on the sufficient condition, the guaranteed cost controller with state feedback is designed. Finally, the LMI toolbox of matlab was used for data simulation, and the corresponding mean-square trajectory map was obtained. Numerical examples show that the obtained simulation results are consistent with the theoretical results, which verifies the effectiveness of the proposed theory.