Soft open points (SOPs) are power electronic devices that may replace conventional normally-open points in distribution networks. They can be used for active power flow control, reactive power compensation, fault isolation, and service restoration through network reconfiguration with enhanced operation flexibility and grid resiliency. Due to unbalanced loading conditions, the voltage unbalance issue, as a common problem in distribution networks, has negative impacts on distribution network operation. In this paper, a control strategy of voltage unbalance compensation for feeders using SOPs is proposed. With the power flow control, three-phase current is regulated simultaneously to mitigate the unbalanced voltage between neighboring feeders where SOPs are installed. Feeder voltage unbalance and current unbalance among three phases are compensated with the injection of negative-sequence and zero-sequence current from SOPs. Especially in response to power outages, three-phase voltage of isolated loads is regulated to be balanced by the control of SOPs connected to the feeders under faults, even if the loads are unbalanced. A MATLAB/Simulink model of the IEEE 13-bus test feeder with an SOP across feeder ends is implemented, and experimental tests on a hardware-in-the-loop platform are implemented to validate the effectiveness of the proposed control strategy.