Large intelligent surface (LIS) equipped with a great number of nearly passive reflecting elements is an emerging technology to improve the wireless coverage and reduce the energy cost. In this paper, we focus on a downlink LIS-assisted MIMO wireless communication system by exploiting the statistical channel state information at base station. Our paper presents the design of covariance matrix of transmitting signals and diagonal phase-shifting matrix of LIS. Since the optimization problem of these two matrices in this paper is non-convex, we propose an alternating optimization algorithm to deal with this intractable problem. For the fixed diagonal phase-shifting matrix, we first obtain the optimal transmit covariance matrix by maximizing the deterministic equivalent of the achievable ergodic rate in the large-system regime. Then, we obtain a locally optimal diagonal phase-shifting matrix using projected gradient ascent method when the transmit covariance matrix is fixed. Simulation results show that the large-system approximate results are good consistent with the original simulation results. We also see that the proposed algorithm can enhance the performance of LIS-assisted MIMO downlink system obviously.