Cell instance segmentation (CIS) via light microscopy and artificial intelligence (AI) is essential to cell and gene therapy-based health care management, which offers the hope of revolutionary health care. An effective CIS method can help clinicians to diagnose neurological disorders and quantify how well these deadly disorders respond to treatment. To address the CIS task challenged by dataset characteristics such as irregular morphology, variation in sizes, cell adhesion, and obscure contours, we propose a novel deep learning model named CellT-Net to actualize effective cell instance segmentation. In particular, the Swin transformer (Swin-T) is used as the basic model to construct the CellT-Net backbone, as the self-attention mechanism can adaptively focus on useful image regions while suppressing irrelevant background information. Moreover, CellT-Net incorporating Swin-T constructs a hierarchical representation and generates multi-scale feature maps that are suitable for detecting and segmenting cells at different scales. A novel composite style named cross-level composition (CLC) is proposed to build composite connections between identical Swin-T models in the CellT-Net backbone and generate more representational features. The earth mover's distance (EMD) loss and binary cross entropy loss are used to train CellT-Net and actualize the precise segmentation of overlapped cells. The LiveCELL and Sartorius datasets are utilized to validate the model effectiveness, and the results demonstrate that CellT-Net can achieve better model performance for dealing with the challenges arising from the characteristics of cell datasets than state-of-the-art models.