Video prediction is an essential vision task due to its wide applications in real-world scenarios. However, it is indeed challenging due to the inherent uncertainty and complex spatiotemporal dynamics of video content. Several state-of-the-art deep learning methods have achieved superior video prediction accuracy at the expense of huge computational cost. Hence, they are not suitable for devices with limitations in memory and computational resource. In the light of Green Artificial Intelligence (AI), more environment friendly deep learning solutions are desired to tackle the problem of large models and computational cost. In this work, we propose a novel video prediction network 3DTransLSTM, which adopts a hybrid transformer-long short-term memory (LSTM) structure to inherit the merits of both self-attention and recurrence. Three-dimensional (3D) depthwise separable convolutions are used in this hybrid structure to extract spatiotemporal features, meanwhile enhancing model efficiency. We conducted experimental studies on four popular video prediction datasets. Compared to existing methods, our proposed 3DTransLSTM achieved competitive frame prediction accuracy with significantly reduced model size, trainable parameters, and computational complexity. Moreover, we demonstrate the generalization ability of the proposed model by testing the model on dataset completely unseen in the training data.