Graph contrastive learning (GCL) has become a hot topic in the field of graph representaion learning. In contrast to traditional supervised learning relying on a large number of labels, GCL exploits augmentation techniques to generate multiple views and positive/negative pairs, both of which greatly influence the performance. Unfortunately, commonly used random augmentations may disturb the underlying semantics of graphs. Moreover, traditional GNNs, a type of widely employed encoders in GCL, are inevitably confronted with over-smoothing and over-squashing problems. To address these issues, we propose GNN-Transformer Cooperative Architecture for Trustworthy Graph Contrastive Learning (GTCA), which inherits the advantages of both GNN and Transformer, incorporating graph topology to obtain comprehensive graph representations. Theoretical analysis verifies the trustworthiness of the proposed method. Extensive experiments on benchmark datasets demonstrate state-of-the-art empirical performance.