A novel coronavirus pneumonia, first identified in Wuhan City and referred to as COVID-19 by the World Health Organization, has been quickly spreading to other cities and countries. To control the epidemic, the Chinese government mandated a quarantine of the Wuhan city on January 23, 2020. To explore the effectiveness of the quarantine of the Wuhan city against this epidemic, transmission dynamics of COVID-19 have been estimated. A well-mixed "susceptible exposed infectious recovered" (SEIR) compartmental model was employed to describe the dynamics of the COVID-19 epidemic based on epidemiological characteristics of individuals, clinical progression of COVID-19, and quarantine intervention measures of the authority. Considering infected individuals as contagious during the latency period, the well-mixed SEIR model fitting results based on the assumed contact rate of latent individuals are within 6-18, which represented the possible impact of quarantine and isolation interventions on disease infections, whereas other parameter were suppose as unchanged under the current intervention. The present study shows that, by reducing the contact rate of latent individuals, interventions such as quarantine and isolation can effectively reduce the potential peak number of COVID-19 infections and delay the time of peak infection.