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For maneuvering target tracking, we propose a novel grey prediction based particle filter (GP-PF), which incorporates the grey prediction algorithm into the standard particle filter (SPF). The basic idea of the GP-PF is that new particles are sampled by both the state transition prior and the grey prediction algorithm. Since the grey prediction algorithm is a kind of model-free method and is able to predict the system state based on historical measurements other than establishing a priori dynamic model, the GP-PF can significantly alleviate the sample degeneracy problem which is common in SPF, especially when it is used for maneuvering target tracking. Simulations are conducted in the context of two typical maneuvering motion scenarios and the results indicate that the overall performance of the proposed GP-PF is better than the SPF and the multiple model particle filter (MMPF) when the tracking accuracy, computational complexity and tracking lost probability are considered. The performance improvements can be attributed to that the GP-PF has both model-based and model-free features.