Pathological diagnosis is the gold standard for tumor diagnosis, and nucleus instance segmentation is a key step in digital pathology analysis and pathological diagnosis. However, the computational efficiency of the model and the treatment of overlapping targets are the major challenges in the studies of this problem. To this end, a neural network model RepSNet was designed based on a nucleus boundary regression and a structural re-parameterization scheme for segmenting and classifying the nuclei in H&E-stained histopathological images. First, RepSNet estimates the boundary position information (BPI) of the parent nucleus for each pixel. The BPI estimation incorporates the local information of the pixel and the contextual information of the parent nucleus. Then, the nucleus boundary is estimated by aggregating the BPIs from a series of pixels using a proposed boundary voting mechanism (BVM), and the instance segmentation results are computed from the estimated nucleus boundary using a connected component analysis procedure. The BVM intrinsically achieves a kind of synergistic belief enhancement among the BPIs from various pixels. Therefore, different from the methods available in literature that obtain nucleus boundaries based on a direct pixel recognition scheme, RepSNet computes its boundary decisions based on some guidances from macroscopic information using an integration mechanism. In addition, RepSNet employs a re-parametrizable encoder-decoder structure. This model can not only aggregate features from some receptive fields with various scales which helps segmentation accuracy improvement, but also reduce the parameter amount and computational burdens in the model inference phase through the structural re-parameterization technique. In the experimental comparisons and evaluations on the Lizard dataset, RepSNet demonstrated superior segmentation accuracy and inference speed compared to several typical benchmark models. The experimental code, dataset splitting configuration and the pre-trained model were released at https://github.com/luckyrz0/RepSNet.