Enhancing state representations can effectively mitigate the issue of low sample efficiency in reinforcement learning (RL) within high-dimensional input environments. Existing methods attempt to improve sample efficiency by learning predictive state representations from sequence data. However, there still remain significant challenges in achieving a comprehensive understanding and learning of information within long sequences. Motivated by this, we introduce a transformer-based state predictive representations auxiliary task that promotes better representation learning through self-supervised goals. Specifically, we design a transformer-based predictive model to establish unidirectional and bidirectional prediction tasks for predicting state representations within the latent space. TSPR effectively exploits contextual information within sequences to learn more informative state representations, thereby contributing to the enhancement of policy training in RL. Extensive experiments demonstrate that the combination of TSPR with off-policy RL algorithms leads to a substantial improvement in the sample efficiency of RL. Furthermore, TSPR outperforms state-of-the-art sample-efficient RL methods on both the multiple continuous control (DMControl) and discrete control (Atari) tasks.