This paper proposes a control technique for a matrix converter topology with three phase fixed grid input and six-phase variable voltage variable frequency output. This proposed technique is based on low frequency Venturini method. A theoretical introduction of the direct matrix converter is presented followed a detailed explanation of the Venturini method and the six-phase matrix converter topology. Finally, a detailed discussion of results is presented (showing the attractive characteristics of the matrix converter), obtained from different simulations using MATLAB/SIMPOWERSYSTEM environment.