Considering that the energy extraction period becomes much smaller than the energy upper state lifetime of the laser gain media, the output laser of high repetition rate regenerative amplifiers contains two-different-energy pulses, which is generally described as the period doubling bifurcation phenomenon. In order to solve this problem, we study the relation between the output laser pulse stabilization of high repetition rate regenerative amplifiers and repetition rate theoretically, and find that the period doubling bifurcation phenomenon can be avoided by increasing the repetition rate of regenerative amplifiers. The experimental results show the period doubling bifurcation phenomenon is avoided when the repetition rate is more than 250 kHz. Furthermore, the regenerative amplification of 1 nJ pulse enenrgy is produced by all-solid-state Nd∶YVO4 crystal semiconductor saturable absorber mirror mode-locked picosecond laser with the repetition rate of 94 MHz. And when the absorbed pump laser is 70 W, we get the frequency tunable (250-500 kHz) picosecond laser. The maximum output average power is 18 W, and the single pulse energy is 36 μJ.