The indeterminate nature of human motion requires trajectory prediction systems to use a probabilistic model to formulate the multi-modality phenomenon and infer a finite set of future trajectories. However, the inference processes of most existing methods rely on Monte Carlo random sampling, which is insufficient to cover the realistic paths with finite samples, due to the long tail effect of the predicted distribution. To promote the sampling process of stochastic prediction, we propose a novel method, called BOsampler, to adaptively mine potential paths with Bayesian optimization in an unsupervised manner, as a sequential design strategy in which new prediction is dependent on the previously drawn samples. Specifically, we model the trajectory sampling as a Gaussian process and construct an acquisition function to measure the potential sampling value. This acquisition function applies the original distribution as prior and encourages exploring paths in the long-tail region. This sampling method can be integrated with existing stochastic predictive models without retraining. Experimental results on various baseline methods demonstrate the effectiveness of our method. The source code is released in this link.