The wind turbine power curve (WTPC) is of great significance for wind power forecasting, condition monitoring, and energy assessment. This paper proposes a novel WTPC modelling method with logistic functions based on quantile regression (QRLF). Firstly, we combine the asymmetric absolute value function from the quantile regression (QR) cost function with logistic functions (LF), so that the proposed method can describe the uncertainty of wind power by the fitting curves of different quantiles without considering the prior distribution of wind power. Among them, three optimization algorithms are selected to make comparative studies. Secondly, an adaptive outlier filtering method is developed based on QRLF, which can eliminate the outliers by the symmetrical relationship of power distribution. Lastly, supervisory control and data acquisition (SCADA) data collected from wind turbines in three wind farms are used to evaluate the performance of the proposed method. Five evaluation metrics are applied for the comparative analysis. Compared with typical WTPC models, QRLF has better fitting performance in both deterministic and probabilistic power curve modeling.