In order to reduce the switching frequencies of power semiconductors and then to increase the efficiency in a three-phase four-wire inverter, the state controllability of a system is investigated by considering the inverter as a switched linear system. It is found that a three-phase four-wire inverter is a three-mode controllable, therein, only three non-zero vectors are required to make the system completely state controllable. With the three operating modes, a novel control strategy, called a three-mode pulse-width modulation (3-MPWM), is proposed in this study. There are three types of 3-MPWMs, that is, 3-MPWM(I), 3-MPWM(II) and 3-MPWM(III). Compared with the conventional space-vector pulse width modulation strategy, the switching frequencies of the proposed 3-MPWMs are significantly reduced by two-thirds, hence, the switching losses of the power semiconductors can be reduced and the efficiency of the inverter can be improved. In addition, the number of operating modes used in 3-MPWM(I) and 3-MPWM(II) is reduced by a half. Finally, simulation and experimental results are conducted to verify the effectiveness of the 3-MPWM strategies.