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In this paper, we concentrate on the direct semi-blind spatial equalizer design for MIMO systems with Rayleigh fading channels. Our aim is to develop an algorithm which can outperform the classical training-based method with the same training information used and avoid the problems of low convergence speed and local minima due to pure blind methods. A general semi-blind cost function is first constructed which incorporates both the training information from the known data and some kind of higher order statistics (HOS) from the unknown sequence. Then, based on the developed cost function, we propose two semi-blind iterative and adaptive algorithms to find the desired spatial equalizer. To further improve the performance and convergence speed of the proposed adaptive method, we propose a technique to find the optimal choice of step size. Simulation results demonstrate the performance of the proposed algorithms and comparable schemes.