Class-agnostic motion prediction methods aim to comprehend motion within open-world scenarios, holding significance for autonomous driving systems. However, training a high-performance model in a fully-supervised manner always requires substantial amounts of manually annotated data, which can be both expensive and time-consuming to obtain. To address this challenge, our study explores the potential of semi-supervised learning (SSL) for class-agnostic motion prediction. Our SSL framework adopts a consistency-based self-training paradigm, enabling the model to learn from unlabeled data by generating pseudo labels through test-time inference. To improve the quality of pseudo labels, we propose a novel motion selection and re-generation module. This module effectively selects reliable pseudo labels and re-generates unreliable ones. Furthermore, we propose two data augmentation strategies: temporal sampling and BEVMix. These strategies facilitate consistency regularization in SSL. Experiments conducted on nuScenes demonstrate that our SSL method can surpass the self-supervised approach by a large margin by utilizing only a tiny fraction of labeled data. Furthermore, our method exhibits comparable performance to weakly and some fully supervised methods. These results highlight the ability of our method to strike a favorable balance between annotation costs and performance. Code will be available at https://github.com/kwwcv/SSMP.