The functions of birefringent filter(BF) narrowing the operation line width of fundamental-wave laser, and improving the stability of frequency-doubling laser are investigated in experiment and theory. The dependence of line width of fundamental wave and frequency-doubling efficiency on the thickness of BF, the thermal source in oscillator, the compensation for thermal effect with BF, and the position of BF in cavity, are investigated experimentally. The experimental results presents that BF not only can narrow the line width of fundamental wave, but also compensate for the birefringence induced by thermal effect of intracavity elements, and decrease the laser loss, further increase dramatically the efficiency of frequency doubling and stability.