This Addressing the efficiency loss and low electrical energy conversion efficiency of the free-piston Stirling linear generator system, we propose an instantaneous power control strategy combining sliding mode control and Newton interpolation prediction algorithms. Through simulation experiments, the Newton interpolation predicted power control is compared with the direct power control algorithm. Compared with the traditional direct power control, this strategy overcomes the efficiency loss caused by the delay of the pulse width modulation switching signal. It reduces the noise and loss due to the non-fixed switching frequency, thereby improving the electrical energy conversion efficiency. Moreover, to enhance the stability and control accuracy of the rectifier output voltage on the generator side, a sliding mode control strategy is introduced into the DC voltage loop. This ensures that the output voltage follows the reference voltage setpoint, resulting in a relatively stable direct current voltage.