Matrix converters as induction motor drivers have received considerable attention in recent years because of its good alternative to voltage source inverter pulse width modulation (VSI-PWM) converters. This paper presents the work carried out in developing a mathematical model for a space vector modulated (SVM) direct controlled matrix converter. The mathematical expressions relating the input and output of the three phase matrix converter are implemented by using MATLAB/SIMULINK. The duty cycles of the switches are modeled using space vector modulation for 0.5 and 0.866 voltage transfer ratios. Simulations of the matrix converter loaded by passive RL load and active induction motor are performed. A unique feature of the proposed model is that it requires very less computation time and less memory compared to the power circuit realized by using actual switches. In addition, it offers better spectral performances, full control of the input power factor, fully utilization of input voltages, improve modulation performance and output voltage close to sinusoidal