The new coronavirus originated in Wuhan, Hubei and rapidly spread to 31 provinces and cities in China and many countries around the world, putting tremendous pressure on world development. When COVID-19 epidemic will end is the issue which draws most attention. Here, this paper applies weighted least squares regression model to study the development characteristics and trends of the number of people under medical observation in Hubei. We modify the predictions for end time of epidemic by combining predicted results of the regression model and actual situation and measure accuracy of model predictions. Applying the above method and using the epidemic data released by Health Commission of Hubei Province, the following conclusions were reached: the day-on-day change rate of the number of people under medical observation showed a linear development trend and has lasted for 46 days; the number of people under medical observation in Hubei dropped to 0 on April 16; after revising the prediction results, the end time of epidemic in Hubei Province should be not earlier than April 5 and not later than April 7. In addition, we find that the weighted linear regression prediction model method is simple and has high prediction accuracy.