Information is not generally distributed uniformly in an image domain. Thus, to make the convolutional neural network focus more on those important, some deformation on convolution windows or feature maps should be applied. Besides, the topology of an image should be preserved from the ideas for defining the convolution operation. However, controlling topology is hard and not convenient for existing methods since they all use vector representation for displacements. In this paper, we proposed Quasi-Conformal Transformer Network using Beltrami representation, which is a strong representation to control the bijectivity and the degree of geometric deformations. Together with our Beltrami Solver Net(BSN), we proposed an end-to-end learnable network, which advantages other works on its power to control the geometric deformation of the feature maps.