To improve the stability of pumping source of optical parametric amplifier, the concept of stable area in the frequency-doubling is proposed, with the numerical simulation of the frequency doubling process. Under certain intensity of the fundamental light, less than the breakdown threshold of the frequency-doubling crystal, the valid length of the frequency-doubling crystal is prolonged with the nonlinear two-pass frequency-doubling or the tandem frequency-doubling, with which the frequency-doubling course is located in the stable area and the highly stable second harmonic output with high conversion efficiency is realized. The experiments prove the above conclusion, and in the experiment the nonlinear two-pass frequency-doubling method is used to ensure the work area of the frequency-doubling in the stable area. The fluctuation of the second harmonic is less than ±2% for the 1064 nm fundamental Gaussian pulse with flutuation ±5.7%, and the conversion efficiency exceeds 70% for high-order Gaussian pulses. The experimental results show that the stability of the second harmonic is near 3 times higher than that of the fundamental light.