Based on the principle of Q-switched intracavity frequency doubled laser, the shape of the second harmonic pulse and the second harmonic unstable light field distribution under the various forms of pump light distribution are studied, and the variation of the second harmonic beam quality is also analyzed. It is found that the light field of Q-switched intracavity frequency-doubled laser is changing in the duration of pulse. In the case of Gaussian type of pump light, it is found that the instability will decrease when the cavity length decreases. And the instability increases by increasing the ratio of the pump light radius and that of the oscillating light, but the average beam quality factor M2 will be greater.