Stochastic Human Motion Prediction (HMP) has received increasing attention due to its wide applications. Despite the rapid progress in generative fields, existing methods often face challenges in learning continuous temporal dynamics and predicting stochastic motion sequences. They tend to overlook the flexibility inherent in complex human motions and are prone to mode collapse. To alleviate these issues, we propose a novel method called STCN, for stochastic and continuous human motion prediction, which consists of two stages. Specifically, in the first stage, we propose a spatio-temporal continuous network to generate smoother human motion sequences. In addition, the anchor set is innovatively introduced into the stochastic HMP task to prevent mode collapse, which refers to the potential human motion patterns. In the second stage, STCN endeavors to acquire the Gaussian mixture distribution (GMM) of observed motion sequences with the aid of the anchor set. It also focuses on the probability associated with each anchor, and employs the strategy of sampling multiple sequences from each anchor to alleviate intra-class differences in human motions. Experimental results on two widely-used datasets (Human3.6M and HumanEva-I) demonstrate that our model obtains competitive performance on both diversity and accuracy.