There exists continued interest in building accurate models of wind turbine power curves for better understanding of performance or assessment of the condition of the turbine or both. Better predictions of the power curve allow increased insight into the operation of the turbine, aid operational decision making, and can be a key feature of online monitoring and fault detection strategies. This work proposes the use of a heteroscedastic Gaussian Process model for this task. The model has a number of attractive properties when modelling power curves. These include, removing the need to specify a parametric functional form for the power curve and automatic quantification of the variance in the prediction. The model exists within a Bayesian framework which exhibits built-in protection against over-fitting and robustness to noisy measurements. The model is shown to be effective on data collected from an operational wind turbine, returning accurate mean predictions ( < 1% normalised mean-squared error) and higher likelihoods than a corresponding homoscedastic model. (C) 2019 The Author(s). Published by Elsevier Ltd.