With the large-scale access of new energy power generation, its grid connection point is weak grid characteristics. Due to the characteristics of its own current source, the grid following inverter reduces its stability margin or even becomes unstable due to its large grid impedance. The grid forming inverter has the voltage and frequency support capability and can operate stably under this working condition, but its power output depends on the frequency deviation, and the dynamic response capability is insufficient. In this paper, the optimized hyperbolic tangent function is used in the active power droop control part, which can replace the traditional linear droop scheme with low application cost. Firstly, the droop control formula with two parameters is constructed according to the characteristics of the hyperbolic tangent function, then the parameter optimization method is proposed, and the calculation and analysis are carried out according to a power grid frequency range. Simulation and comparison of the active power output of the inverter with hyperbolic tangent droop control and traditional droop control at different grid frequencies. The response speed of the inverter output active power is faster and the overshoot is reduced.