The drawback of classical matrix converter having low voltage transfer ratio is studied and a topology of a new matrix converter called as a Cuk matrix converter is proposed. The basic configuration of this new topology and its fundamental are firstly introduced, the analytic expression concerning functions relation of voltage transfer ratio to duty cycle is deduced, and the basic design method of double-loop control strategy is expounded. Finally the validity and feasibility of the new topology are tested by simulation.The results show that the output voltage and frequency can be modulated optionally by the new converter, of which the voltage transfer ratio can be greater than 1, or lower than 1, and an ideal sine wave can be directly obtained without filtering. Thus the inherent problem of classical matrix converter having low voltage transfer ratio is effectively solved by this study, which is of certain practical importance.