Spatiotemporal predictive learning, which predicts future frames through historical prior knowledge with the aid of deep learning, is widely used in many fields. Previous work essentially improves the model performance by widening or deepening the network, but it also brings surging memory overhead, which seriously hinders the development and application of this technology. In order to improve the performance without increasing memory consumption, we focus on scale, which is another dimension to improve model performance but with low memory requirement. The effectiveness has been widely proved in many CNN-based tasks such as image classification and semantic segmentation, but it has not been fully explored in recent RNN models. In this paper, learning from the benefit of multi-scale, we propose a general framework named Multi-Scale RNN (MS-RNN) to boost recent RNN models for spatiotemporal predictive learning. By integrating different scales, we enhance the existing models with both improved performance and greatly reduced overhead. We verify our MS-RNN framework by exhaustive experiments with 6 popular RNN models (ConvLSTM, TrajGRU, PredRNN, PredRNN++, MIM, and MotionRNN) on 4 different datasets (Moving MNIST, KTH, TaxiBJ, and HKO-7). The results show the efficiency that the RNN models incorporating our framework have much lower memory cost but better performance than before. Our code is released at https://github.com/mazhf/MS-RNN.