Floating wind turbines are continuously subjected to combined wind and wave loads during their offshore service life. The complex environment in deep and far-reaching seas leads to frequent occurrences of non-collinear wind and wave phenomena, which pose significant challenges to the service reliability of floating wind turbines. Therefore, this paper selects typical wind-wave misalignment angle conditions to conduct reliability analysis on the drive train system of floating wind turbines. Taking the drive train of a 6.2 MW floating wind turbine as the research object, a rigid-flexible coupled multi-body dynamics model of the drive train is established. The influence mechanism of wind-wave misalignment angles on the vibration characteristics of the drive train system is studied, and the variation laws of vibration response and service reliability of the gear transmission system under different wind-wave misalignment angles are revealed. The research results show that when the wind-wave misalignment angle increases from 0° to 90°, the vibration displacement, vibration velocity, vibration acceleration and their corresponding root mean square (RMS) values of all stages of gears in the drive train show a monotonically increasing trend. Among them, the vibration is the mildest under the 0° collinear condition, while the most severe under the 90° misalignment condition. The vibration acceleration of the intermediate-stage planetary gear is significantly higher than that of other gears. Without considering the gear strength degradation, the reliability of the floating wind turbine drive train decreases continuously with the increase of wind-wave misalignment angle. At the 25th year, the reliability of the drive train is 0.8193 under the 0° condition and 0.7886 under the 90° condition, and the reliability reduction rate increases from 18.07% to 21.14%. After considering the gear strength degradation effect, the most significant reliability attenuation occurs in the 10-20 year period, and the reliability under all wind-wave misalignment angle conditions drops to approximately 0.35 by the 25th year.