Floating wind farms (FOWF) are one of the main forms of wind energy utilization in the deep-sea areas. This study proposes a multi-objective reposition control approach for floating wind farms. Firstly, an imperial wake model of floating wind turbines is constructed considering the effects of wind and wave conditions. A nonlinear model of a catenary mooring line is subsequently constructed. Furthermore, a multi-objective location optimization method is proposed that allows for the tradeoff between the maximum power of the farm and the minimum drift distance of the turbines accounting for the time-varying wind speed and direction. The results of the proposed approach are then compared with those of traditional methods. The findings indicate that time-varying changes in wind have a significant influence on the optimal position of turbines. It can decrease the maximum drift distance by approximately 7 % when considering temporal variations in wind. Furthermore, the proposed reposition control maintains almost the same power output of the wind farm while reducing the total offset distance from the equilibrium point of turbines by approximately 11 %. The impact of mooring orientation, natural length, turbine spacing, and wave speed on the control performance are also elucidated.