Imitation learning offers a high-performance and versatile solution for addressing various complex decision-making problems in the real world. Generative Adversarial Imitation Learning (GAIL) is a highly potential algorithmic framework in the field of imitation learning, where high-performance policies can be obtained by computing imitation rewards based on a given series of expert datasets. However, existing algorithms based on the GAIL framework predominantly focus on the current state and seldom consider the influence of time series on the acquisition of imitation rewards. Using time series is an effective and efficient method to solve the long-term dependency problem in long-horizon robotic tasks. The algorithm we propose combines the GAIL algorithm with time series, utilizing a Transformer encoder to obtain representations of state sequences. It generates imitation rewards using an attention-based representation. To address the instability in the imitation rewards caused by the large model size, we employed a range mapping method to enhance stability. The GAIL algorithm, with our proposed imitation reward, achieves commendable results across DeepMind Control Suite. We also experimented with different lengths of time series and sequence models, demonstrating the effectiveness of integrating time series with the GAIL framework using transformers. Our method attained 92.53% of the expert reward in the walker_run environment, significantly outperforming the GAIL framework using Temporal Convolutional Network (TCN), which only achieved 10.28% of the expert reward.