Soft open point (SOP) is a key power electronic device to improve the flexibility and stability of the distribution network and is becoming a research hotspot. The traditional double closed-loop control of SOP has a complex structure, difficult process of parameter design, and poor output power quality. To solve these problems, finite control set model predictive control (FCS-MPC) has been adopted. Since FCS-MPC involves a large amount of calculation and experiences delay in current tracking, an improved FCS-MPC with delay compensation is proposed for three-port SOP in this paper to replace the inner loop current control strategy. Improved model predictive control combines the two-step prediction method based on the voltage vector and vector angle compensation method. The vector method is used to construct a mathematical model and a prediction model of three-port SOP. Based on FCS-MPC, the two-step prediction method that takes voltage as the target is used to compensate for the current delay problem, and the amount of calculation is reduced by converting the control target. Meanwhile, the vector angle compensation method is used to compensate the future reference value. Finally, a simulation model is built in MATLAB/Simulink. The simulation results under steady state and dynamic conditions show that the proposed strategy can effectively improve the current delay and reduce the amount of calculation. Furthermore, it has better current tracking accuracy and faster dynamic response speed.