Pedestrian trajectory prediction is a key technology in many applications such as video surveillance, social robot navigation, and autonomous driving, and significant progress has been made in this research topic. However, there remain two limitations of previous studies. First, with the continuation of time, the prediction error at each time step increases significantly, causing the final displacement error to be impossible to ignore. Second, the prediction results of multiple pedestrians might be impractical in the prediction horizon, i.e., the predicted trajectories might collide with each other. To overcome these limitations, this work proposes a novel trajectory prediction method called CSR, which consists of a cascaded conditional variational autoencoder (CVAE) module and a socially-aware regression module. The cascaded CVAE module first estimates the future trajectories in a sequential pattern. Specifically, each CVAE concatenates the past trajectories and the predicted points so far as the input and predicts the location at the following time step. Then, the socially-aware regression module generates offsets from the estimated future trajectories to produce the socially compliant final predictions, which are more reasonable and accurate results than the estimated trajectories. Moreover, considering the large model parameters of the cascaded CVAE module, a slide CVAE module is further exploited to improve the model efficiency using one shared CVAE, in a slidable manner. Experiments results demonstrate that the proposed method exhibits improvements over state-of-the-art method on the Stanford Drone Dataset (SDD) and ETH/UCY of approximately 38.0% and 22.2%, respectively.