The COVID-19 pandemic, which broke out in Wuhan, China, in 2019, was declared an international public health emergency by the World Health Organization on January 31, 2020. The outbreak on the Diamond Princess cruise ship had appeared first as a cluster infection outside China during the early pandemic. The incident occurred on February 1, 2020, involved an 80-year-old Hong Kong man who was diagnosed with COVID-19. The cruise ship docked in Yokohama, Japan, for 14 days of onboard quarantine; however, cluster infection outbroke rapidly. We constructed a SIR mathematical model and conducted an epidemiological study of the COVID-19 outbreak on the Diamond Princess cruise ship, covering the period from February 5 (start of quarantine) to February 20 (completion of 14-day quarantine). We estimated the basic reproduction number (R 0 ) using a novel method of nonlinear least-squares curve fitting under Microsoft Excel Solver. The 95% confidence interval (CI) values were estimated by the jackknife procedures. Six hundred thirty-four (17.1%) cases were diagnosed in a total population of 3711 cruise passengers, and 328 (51.7%) cases were asymptomatic. As of April 24, 2020, 712 cases had been diagnosed and 14 (1.96%) deaths had occurred. The R 0 with 95% CI of the COVID-19 outbreak was 3.04 (2.72-3.36). Without an evacuation plan for passengers and crew, we estimated the total number of cumulative cases would reach 3498 (CI, 3464-3541). If the R 0 value was reduced by 25% and 50%, the cumulative cases would be reduced to 3161 (CI, 3087-3254) and 967 (CI, 729-1379), respectively. The abovementioned R 0 value was estimated from the original Wuhan strain. Cruise conditions would accelerate the spread of infectious diseases and were not suitable for onboard quarantine. Early evacuation and isolation of all passengers and crew members would reduce the R 0 value and avoid further infections.