A multiple-input multiple-output (MIMO) wiretap channel in the presence of one multiple-antenna eavesdropper is considered. We assume that imperfect channel state information (CSI) on the legitimate link and only statistical CSI of the eavesdropper channel are available at the transmitter. This paper addresses the issue of optimal input covariance matrix design that maximizes the secrecy rate subject to the total power constraint. The secrecy rate maximization (SRM) is studied under a relaxed assumption on the perfect CSI.We reformulate the SRM problem and propose an alternating optimization (AO) algorithm to find the optimal input covariance matrix. Simulation results are presented to validate the effectiveness of the proposed approach. The impact of the channel estimation error is investigated.