This paper proposes the space vector pulse width modulation technique of a matrix converter topology with three phase fixed grid input and seven phase variable voltage variable frequency output. Voltage source inverter is generally used for feeding multi-phase drives. Multi-phase matrix converter is proposed in this paper as a new solution for feeding multi phase system. The paper develops the complete space vector algorithm of the proposed multi-phase matrix converter topology. The developed space vector model suggests 221 possible switching combination vectors. After imposing mathematical constraints the number of switching combinations reduce to 2184 active and three zero vectors. The complete space vector PWM algorithm is developed in the paper. The feasibility of the proposed algorithm is proved using analytical, simulation and real-time approach.