The pandemic of coronavirus disease 2019 (COVID-19) has threatened the social and economic structure all around the world. Generally, COVID-19 has three possible transmission routes, including pre-symptomatic, symptomatic and asymptomatic transmission, among which the last one has brought a severe challenge for the containment of the disease. One core scientific question is to understand the influence of asymptomatic individuals and of the strength of control measures on the evolution of the disease, particularly on a second outbreak of the disease. To explore these issues, we proposed a novel compartmental model that takes the infection of asymptomatic individuals into account. We get the relationship between asymptomatic individuals and critical strength of control measures theoretically. Furthermore, we verify the reliability of our model and the accuracy of the theoretical analysis by using the real confirmed cases of COVID-19 contamination. Our results, showing the importance of the asymptomatic population on the control measures, would provide useful theoretical reference to the policymakers and fuel future studies of COVID-19.