Compared with a traditional three-leg current source inverter (3L-CSI), the four-leg current source inverter (4L-CSI) can supply unbalanced loads. To reduce the losses of the 3L-CSI, the two-third pulse-width modulation (2/3-PWM) can be used to reduce the dc-link current and switching frequency. In this paper, an algebraic modulation strategy called three-quarter pulse-width modulation (3/4-PWM) is proposed for 4L-CSI based on the 2/3-PWM. Through matrix operation, the general solution of the modulation matrix is obtained and the duty cycles can be calculated under specific constraints. It can reduce the circuit conduction loss and switching loss by reducing the dc-link current and reducing the switching frequency. To verify the effectiveness of the proposed strategy, time-domain simulations are carried out by using MATLAB/Simulink under balanced and unbalanced load cases.