This paper considers a MIMO secure wireless communication system aided by the physical layer security technique of sending artificial noise (AN). To further enhance the system security performance, the advanced intelligent reflecting surface (IRS) is invoked in the AN-aided communication system, where the base station (BS), legitimate information receiver (IR) and eavesdropper (Eve) are equipped with multiple antennas. With the aim for maximizing the secrecy rate (SR), the transmit precoding (TPC) matrix at the BS, covariance matrix of AN and phase shifts at the IRS are jointly optimized subject to constrains of transmit power limit and unit modulus of IRS phase shifts. Then, the secrecy rate maximization (SRM) problem is formulated, which is a non-convex problem with multiple coupled variables. To tackle it, we propose to utilize the block coordinate descent (BCD) algorithm to alternately update the TPC matrix, AN covariance matrix, and phase shifts while keeping SR non-decreasing. Specifically, the optimal TPC matrix and AN covariance matrix are derived by Lagrangian multiplier method, and the optimal phase shifts are obtained by Majorization-Minimization (MM) algorithm. Since all variables can be calculated in closed form, the proposed algorithm is very efficient. We also extend the SRM problem to the more general multiple-IRs scenario and propose a BCD algorithm to solve it. Finally, simulation results validate the effectiveness of system security enhancement via an IRS.