This paper presents a new technique for filtering current harmonics in three-phase four-wire networks based on the usage of a four-branch star (FBS) filter topology. Based on single-phase inductors and capacitors, the specific layout of the FBS filter topology allows achieving a power filter with two independent and simultaneous resonance frequencies, i.e., one for positive-/negative-sequence and another one for zero-sequence components. The FBS filter topology can work either as a passive filter, when only passive components are employed, or as a hybrid filter, when its performance is improved by integrating a power converter into its structure. This paper analyzes the FBS topology and presents fundamental concepts regarding the control of a generic FBS hybrid power filter. A neutral current hybrid power filter and var compensator is presented as an illustrative example applying the FBS filtering topology to a three-phase four-wire system. An extensive evaluation using simulation and experimental results are conducted in this work to validate the good performance of the proposed solution for canceling current harmonics flowing through the neutral conductor.