There has been an outbreak of coronavirus disease (COVID-19) in Wuhan city, Hubei province, China since December 2019. Cases have been exported to other parts of China and many other countries. We provide estimates of the daily trend in the size of the epidemic in Wuhan based on detailed information of 10,940 confirmed cases outside Hubei province. In this modelling study, we first estimate the epidemic size in Wuhan from January 11, 2020, to February 13, 2020, based on the confirmed cases outside Hubei province that left Wuhan by January 23, 2020. Since some confirmed cases have no information on whether they visited Wuhan before, we adjust for these missing values. We then calculate the reporting rate in Wuhan from January 20, 2020, to February 13, 2020. Finally, we estimate the date when the first patient was infected. We estimate the number of cases that should be reported in Wuhan by January 11, 2020, is 4,094 (95% confidence interval [CI]: 3,980 – 4,211) and 58,153 (95% CI: 56,532 – 59,811) by February 13, 2020. The reporting rate has grown rapidly from 1.41% (95% CI: 1.37% - 1.45%) on January 20, 2020, to 32.15% (95% CI: 31.26% - 33.07%) on February 11, 2020, and reaches 61.89% (95% CI: 60.17% - 63.66%) on February 13, 2020. The date of first infection is estimated as November 30, 2019. The estimated reporting rate has increased rapidly to over 60% on February 13, 2020, mainly because the inclusion of 14,031 clinically diagnosed cases in the case reports of Wuhan. This might indicate that clinical diagnosis could be a good complement to the current method of confirmation. The currently reported number of 35,991 cases as of February 13, 2020, is still far below our estimate of 58,153. There may still be a lot of unreported cases. More thorough screening of all patients with a mild or moderate symptoms of respiratory diseases should be conducted to better control the spread of COVID-19.