Three-phase four-leg voltage-source converters are used in inverter, rectifier and active filter applications to control the neutral current caused by unbalanced or nonlinear loads. From the modulation point of view, a four-leg converter can be considered as a four-phase system. Hence, the modulation task can be carried out with a generic multiphase modulation algorithm. In this paper, a recent multilevel multiphase space vector PWM algorithm with switching state redundancy is particularized for multilevel three-phase four-leg converters. The obtained algorithm is compared with an existing three-dimension modulation technique showing important similarities. Finally, the new algorithm is implemented in a low-cost field-programmable gate array and it is tested with a five-level cascaded full-bridge inverter.