Coronavirus disease 2019 (COVID-19) has brought dramatic changes in our daily life, especially in human mobility since 2020. As the major component of the integrated transport system in most cities, taxi trips represent a large portion of residents’ urban mobility. Thus, quantifying the impacts of COVID-19 on city-wide taxi demand can help to better understand the reshaped travel patterns, optimize public-transport operational strategies, and gather emergency experience under the pressure of this pandemic. To achieve the objectives, the Geographically and Temporally Weighted Regression (GTWR) model is used to analyze the impact mechanism of COVID-19 on taxi demand in this study. City-wide taxi trip data from August 1st, 2020 to July 31st, 2021 in New York City was collected as model’s dependent variables, and COVID-19 case rate, population density, road density, station density, points of interest (POI) were selected as the independent variables. By comparing GTWR model with traditional ordinary least square (OLS) model, temporally weighted regression model (TWR) and geographically weighted regression (GWR) model, a significantly better goodness of fit on spatial-temporal taxi data was observed for GTWR. Furthermore, temporal analysis, spatial analysis and the epidemic marginal effect were developed on the GTWR model results. The conclusions of this research are shown as follows: (1) The virus and health care become the major restraining and stimulative factors of taxi demand in post epidemic era. (2) The restraining level of COVID-19 on taxi demand is higher in cold weather. (3) The restraining level of COVID-19 on taxi demand is severely influenced by the curfew policy. (4) Although this virus decreases taxi demand in most of time and places, it can still increase taxi demand in some specific time and places. (5) Along with COVID-19, sports facilities and tourism become obstacles on increasing taxi demand in most of places and time in post epidemic era. The findings can provide useful insights for policymakers and stakeholders to improve the taxi operational efficiency during the remainder of the COVID-19 pandemic.