Predicting the future trajectories of multiple pedestrians in certain scenes is critical for autonomous moving platforms (like, self-driving cars and social robots). In this paper, we propose a novel Generative Adversarial Network model with Transformers, which simulates the pedestrian distribution to capture the uncertainty of the predicted paths and generate more reasonable future trajectories. The design of our method includes a generator and a discriminator. The generator mainly contains an encoder, a decoder, and a prediction module. Specifically, the encoder and the decoder comprise multihead convolutional self-attention to learn the sequence of historical movement, and the prediction module incorporates the Mish Feed-Forward Network to yield the predicted target. The discriminator takes both the predicted paths and ground truth as input, classifies them as socially acceptable or not. Experimental results show that the proposed method consistently boosts the performance of trajectory forecasting, and our framework surpasses several existing baselines by evaluating the results on various data sets. Code is available at https://github.com/lzz970818/Trajectory-Prediction.