In this paper, a reconfigurable intelligent surface (RIS)-assisted MIMO wireless secure commu-nication system is considered, in which a base sta-tion (BS) equipped with multiple antennas exploits statistical channel state information to communicate with a legitimate multi-antenna user, in the presence of an eavesdropper, also equipped with multiple an-tennas. We firstly obtain an analytical expression of the ergodic secrecy rate based on the results of large-dimensional random matrix theory. Then, a jointly al-ternating optimization algorithm with the method of Taylor series expansion and the projected gradient as-cent method is proposed to design the transmit covari-ance matrix at the BS, as well as the diagonal phase-shifting matrix to maximize the ergodic secrecy rate. Simulations are conducted to demonstrate the accu-racy of the derived analytical expressions, as well as the superior performance of our proposed algorithm.