In this paper, we present a transmission scheme for a multiple-input multiple-output (MIMO) quasi-static fading channel with imperfect channel state information at the transmitter (CSIT). In this scheme, we develop a precoder structure to exploit the available CSIT and apply spatial coupling for further performance enhancement. We derive an analytical evaluation method based on extrinsic information transfer (EXIT) functions, which provides convenience for our precoder design. Furthermore, we observe an area property indicating that, for a spatially coupled system, the iterative receiver can perform error-free decoding even the original uncoupled system has multiple fixed points in its EXIT chart. This observation implies that spatial coupling is useful to alleviate the uncertainty in CSIT which causes difficulty in designing LDPC code based on the EXIT curve matching technique. Numerical results are presented, showing an excellent performance of the proposed scheme in MIMO fading channels with imperfect CSIT.