Abstract: Floating wind turbines are deployed in deep seas, whose supporting platforms undergo prominent low-frequency motions. Different from fixed offshore wind turbines, the rotor inflow is disturbed by platform pitch and surge apart from ambient wind speed, leading to intense power fluctuation, strong nonlinearity and multivariate coupling. Traditional power curve models ignore platform motion impacts; conventional recurrent neural networks and vanilla Transformers are incompetent in depicting cross-dimensional variable correlations, while pure data-driven models easily violate physical principles under sparse working conditions. This paper thereby proposes a floating wind turbine power prediction method combining physical prior knowledge and Crossformer network. Wind speed is corrected via platform pitch angular velocity to reflect actual rotor inflow. The theoretical wind-power curve constructed by PCHIP serves as physical constraints during model training. The Crossformer architecture is employed to extract long-term temporal dependencies and coupling characteristics of operational parameters and platform attitudes. A hybrid training framework with dual loss functions and dynamic weight adjustment is established. Experimental results show that the PI-Crossformer achieves MAPE of 3.06%, MAE of 73.67 kW, RMSE of 135.01 kW and R² of 0.9968 in one-hour multi-step prediction, which balances forecasting accuracy, physical rationality and multi-step prediction stability.