This paper investigates the finite-time H control problem for discrete-time Markovian jump linear systems with time delay and norm-bounded exogneous disturbance. The stochastic finite-time boundness is achieved by employing an average dwell time approach, which has more design freedom by allowing the stochastic Lyapunov-like function (SLLF) to increase more slowly during the running time of each operation mode. Note that the SLLF increases at every jumping instant rather than at every sampling time instant. Sufficient conditions for the solvability of the controller, which are dependent or independent on the time delay, are given in terms of linear matrix inequalities. Numerical examples are given to verify the efficiency of the proposed method.