Matrix converter has low voltage transfer ratio, especially those with non-sinusoidal output. The research of matrix converters driving BLDC (brushless DC) motors with rectangular phase current is found only in one paper. But the voltage transfer ratio (UPN/2Uim, UPN is the equivalent output DC voltage, i.e. the leg-leg voltage of BLDC, and Uim is the peak input phase voltage, which is different from the matrix converter with sinusoidal output) is only 0.65[1]. This paper presents an input current SVPWM method, which enables the voltage transfer ratio to reach 0.75. Besides, a new over-modulation strategy to increase the voltage transfer ratio further is also presented, which can increase the voltage transfer ratio from 0.75 (in linear modulation region) to 0.825 (in over-modulation region) theoretically. With the proposed over-modulation method, voltage transfer ratio of the matrix converter can be increased to raise the speed of BLDC motor. The feasibility and validity of the strategy has been verified by simulation.