Manoeuvring target tracking faces the challenge caused by the target motion model uncertainty, i.e., unknown model types or uncertain model parameters. Multiple-model (MM) methods have been generally considered to deal with this challenge, in which a bank of elemental filters is run simultaneously to provide a joint decision and estimation of motion model and localisation. However, if the uncertainty of the target trajectory increases, such as the target moves under mixed manoeuvring behaviours with time-varying parameters, more filters with different model assumptions have to be taken into account to match the motion of the target, which may lead to prohibitive computational complexity. To address this problem, we establish a training based algorithm which can learn the actual motion model as a Gaussian process (GP) regression. Then, by integrating the trained GP into the particle filter (PF), a GP-PF based tracking method is developed to track the manoeuvring targets in real-time. Monte Carlo experiments show that the proposed method had much lower tracking root mean square error (RMSE) and robustness compared with the most commonly used MM methods.