With the consideration of the second and the third order nonlinear effect, the Lugiato-Lefeve equation which describes the field evolution of the fundamental frequency wave and the second harmonic wave is introduced. Based on the Lugiato-Lefeve equation, the generation of the second harmonic wave in the SiN microresonator is analyzed, and the effect of the each parameter on the dual field is studied. Simulation results indicate that the stable field of the fundamental frequency wave is of flat top pulse, and the field of the second harmonic wave is of sinusoidal distribution. When the detuning parameter increases, the power of the dual wave inside the microresonator oscillates, and the stable power weakens, the stable light field is periodically varied. Moreover, the chaos emerges as detuning parameter becomes large. The stable field can be generated in the microresonator with the weak pump power. However, because of the high pump power, the dispersion and nonlinear effect are enhanced, resulting in the periodic light field. Furthermore, the oscillation of the dual power curve is aggravated, as the pump power increases. In addition, the turning patterns can be observed by choosing the special dimension of microresonator. Theoretical analysis results are significant for studying the generation of the second harmonic wave in the microresonator.