The outbreak of COVID-19 caused by SARS-CoV-2 in Wuhan and other cities of China is a growing global concern. Delay in diagnosis and limited hospital resources lead to a rapid spread of COVID-19. In this study, we investigate the effect of delay in diagnosis on the disease transmission with a new formulated dynamic model. Sensitivity analyses and numerical simulations reveal that, improving the proportion of timely diagnosis and shortening the waiting time for diagnosis can not eliminate COVID-19 but can effectively decrease the basic reproduction number, significantly reduce the transmission risk, and effectively prevent the endemic of COVID-19, e.g., shorten the peak time and reduce the peak value of new confirmed cases and new infection, decrease the cumulative number of confirmed cases and total infection. More rigorous prevention measures and better treatment of patients are needed to control its further spread, e.g., increasing available hospital beds, shortening the period from symptom onset to isolation of patients, quarantining and isolating the suspected cases as well as all confirmed patients.