In this paper, we establish a compartmental model for the transmission of COVID-19 with both symptomatic and asymptomatic infections. The difference is that in our model, we consider the infection caused by multiple contacts with asymptomatic infected population. Through the dynamic analysis of the model, we found that when there is only one contact with an asymptomatic infected people, the system has a unique threshold to control the disease. When there is two contact with asymptomatic infected population, the system will undergo forward bifurcation, backward bifurcation, saddle-node bifurcation, supercritical Hopf bifurcation, subcritical Hopf bifurcation, and Bogdanov-Takens bifurcation with codimension 2. Finally, we give The complete bifurcation diagram and global phase diagram of the system, and the biological significance of our results are also given.