Harvesting offshore wind energy resources using floating vertical axis wind turbines (VAWTs) has attracted an increasing interest in recent years. Due to its potential impact on fatigue damage, the aerodynamic damping should be considered in the preliminary design of a floating VAWT based on the frequency domain method. However, currently the study on aerodynamic damping of floating VAWTs is very limited. Due to the essential difference in aerodynamic load characteristics, the aerodynamic damping of a floating VAWT could be different from that of a floating horizontal axis wind turbine (HAWT). In this study, the aerodynamic damping of floating VAWTs was studied in a fully coupled manner, and its influential factors and its effects on the motions, especially the pitch motion, were demonstrated. Three straight-bladed floating VAWTs with identical solidity and with a blade number varying from two to four were considered. The aerodynamic damping under steady and turbulent wind conditions were estimated using fully coupled aero-hydro-servo-elastic time domain simulations. It is found that the aerodynamic damping ratio of the considered floating VAWTs ranges from 1.8% to 5.3%. Moreover, the aerodynamic damping is almost independent of the rotor azimuth angle, and is to some extent sensitive to the blade number.