The COVID-19 outbreak on the Diamond Princess (DP) cruise ship has provided empirical data to study the transmission potential of COVID-19 with the presence of pre/asymptomatic cases. We studied the changes in R.sub.0 on DP from January 21 to February 19, 2020 based on chain binomial models under two scenarios: no quarantine assuming a random mixing condition, and quarantine of passengers in cabins-passengers may get infected either by an infectious case in a shared cabin or by pre/asymptomatic crew who continued to work. Estimates of R.sub.0 at the beginning of the epidemic were 3.27 (95% CI, 3.02-3.54) and 3.78 (95% CI, 3.49-4.09) respectively for serial intervals of 5 and 6 days; and when quarantine started, with the reported asymptomatic ratio 0.505, R.sub.0 rose to 4.18 (95%CI, 3.86-4.52) and 4.73 (95%CI, 4.37-5.12) respectively for passengers who might be exposed to the virus due to pre/asymptomatic crew. Results confirm that the higher the asymptomatic ratio is, the more infectious contacts would happen. We find evidence to support a US CDC report that "a high proportion of asymptomatic infections could partially explain the high attack rate among cruise ship passengers and crew." Our study suggests that if the asymptomatic ratio is high, the conventional quarantine procedure may not be effective to stop the spread of virus.