Predicting batteries' future degradation is essential for developing durable electric vehicles. The technical challenges arise from the absence of full battery degradation model and the inevitable local aging fluctuations in the uncontrolled environments. This paper proposes a base model-oriented gradient-correction particle filter (GC-PF) to predict aging trajectories of Lithium-ion batteries. Specifically, under the framework of typical particle filter, a gradient corrector is employed for each particle, resulting in the evolution of particle could follow the direction of gradient descent. This gradient corrector is also regulated by a base model. In this way, global information suggested by the base model is fully utilized, and the algorithm's sensitivity could be reduced accordingly. Further, according to the prediction deviations of base model, weighting factors between the local observations and base model can be updated adaptively. Four different battery datasets are used to extensively verify the proposed algorithm. Quantitatively, the RMSEs of GC-PF can be limited to 1.75%, which is 44% smaller than that of the conventional particle filter. In addition, the consistency of predictions when using different size of training data is also improved by 32%. Due to the pure data-driven nature, the proposed algorithm can also be extendable to other battery types.