Recent MLP-Mixer has a good ability to handle long-range dependencies, however, to have a good performance, one requires huge data and expensive infrastructures for the pre-training process. In this study, we proposed a novel model for nuclei image segmentation namely Axial Convolutional-MLP Mixer, by replacing the token mixer of MLP-Mixer with a new operator, Axial Convolutional Token Mix. Specifically, in the Axial Convolutional Token Mix, we inherited the idea of axial depthwise convolution to create a flexible receptive field. We also proposed a Long-range Attention module that uses dilated convolution to extend the convolutional kernel size, thereby addressing the issue of long-range dependencies. Experiments demonstrate that our model can achieve high results on small medical datasets, with Dice scores of 90.20% on the GlaS dataset, 80.43% on the MoNuSeg dataset, and without pre-training. The code will be available at https://github.com/thanhthu152/AC-MLP.