The influence of gain coefficient on the output characteristics of ring cavity laser is researched by numerical simulation. At first, the light intensity equation of the ring cavity laser model after transverse effect is given. And then, the dynamical behaviors of the laser system are determined by simulating the evolution of the Lyapunov exponent with the gain coefficient, and the formation of laser pattern of ring cavity laser after light transverse effect is demonstrated. At last, the influence of gain coefficient on the output characteristics of ring cavity laser is illustrated by simulating the laser patterns under different gain coefficients.