Aimed at the problems that matching speed is slow and matching accuracy is low in airborne miniaturized RF power supply in plasma stealth. Through analyzing rf circuit impedance matching process, an optimization objective function is put forward. According to the characteristic curve of circuit output active power and matching capacitance, the peak value of objective function is founded. An improved terminal sliding mode extremum search algorithm is designed by combining switching links with terminal sliding mode control, the optimal values of L shape matching network and the maximum power output for rf source are obtained. Moreover, the stability of this control method is proved. Based on the optimization of the sliding mode extremum, the threshold function is set when switching between mode 2 and mode 3 is made, and the terminal sliding mode surface is added at the sliding mode oscillation stage to reduce the steadystate error of the system, reducing the steadystate oscillation amplitude of the system, increasing the convergence speed and simplifying the computational complexity of the system. Compared with the traditional sliding mode method, the simulation results show that the proposed method is valid.