Optimal design of training sequences for Multiple-Input Multiple-Output (MIMO) channel estimation is considered. The channel is assumed to be frequency-selective and obey block-fading law with both spatial fading correlation and multipath tap gain correlation known at both the transmitter and receiver. To minimize the channel estimation error, optimal training sequences are designed to exploit full information of channel correlation under the criterion of Minimum Mean Square Error (MMSE). It is investigated that channel correlation is helpful to decrease the estimation error and the proposed training sequences have good performance via simulations.