In this paper, we consider an intelligent reflecting surface (IRS) assisted Guassian multiple-input multiple-output (MIMO) wiretap channel (WTC), and focus on enhancing its secrecy rate. Due to MIMO setting, all the existing solutions for enhancing the secrecy rate over multiple-input single-output WTC completely fall to this work. Furthermore, all the existing studies are simply based on an ideal assumption that full channel state information (CSI) of eavesdropper (Ev) is available. Therefore, we propose numerical solutions to enhance the secrecy rate of this channel under both full and no Ev's CSI cases. For the full CSI case, we propose a barrier method and one-by-one (OBO) optimization combined alternating optimization (AO) algorithm to jointly optimize the transmit covariance R at transmitter (Tx) and phase shift coefficient Q at IRS. For the case of no Ev's CSI, we develop an artificial noise (AN) aided joint transmission scheme to enhance the secrecy rate. In this scheme, a bisection search (BS) and OBO optimization combined AO algorithm is proposed to jointly optimize R and Q. Such scheme is also applied to enhance the secrecy rate under a special scenario in which the direct link between Tx and receiver/Ev is blocked due to obstacles. In particular, we propose a BS and minorization-maximization (MM) combined AO algorithm with slightly faster convergence to optimize R and Q for this scenario. Simulation results have validated the monotonic convergence of the proposed algorithms, and it is shown that the proposed algorithms for the IRS-assisted design achieve significantly larger secrecy rate than the other benchmark schemes under full CSI. When Ev's CSI is unknown, the secrecy performance of this channel also can be enhanced by the proposed AN aided scheme, and there is a trade-off between increasing the quality of service at Rx and enhancing the secrecy rate.