Back-to-back (B2B) converter is adopted widely in soft open point (SOP) to improve the flexibility of distribution system and support the voltage of critical load under power grid outage. However, B2B converter has the drawbacks of large volume and high cost. Therefore, the hybrid SOP is introduced in this paper, which is composed of an interconnection switch and B2B converter with smaller capacity. The transfer process of how hybrid SOP changes into supporting load voltage when power grid outage occurs. To guarantee the continuous power supply of critical load, the transient short-circuit loop is inevitable in the hybrid SOP during transfer process. Based on the equivalent circuit, the transient current is calculated, according to which two kinds of control strategies for converter at outage side to power all the loads are proposed. With the proposed method, the duration time that converter powers full the loads alone decreases and the overcurrent can also be restrained. Two kinds of control strategies are compared from the respects of stability and overcurrent suppression in simulation. The simulation results of the whole transfer process are provided as well.