An U-shaped dual-energy computed tomography (DECT) material decomposition network, called DM-Unet, that combines a selective state spaces model Mamba and efficiency channel attention module is proposed in this paper. The network uses a visual state space module that introduces a channel attention mechanism to capture feature information, adjusts the weights of different levels for feature information in a block through adjustable parametric residual connections, and reduces the gradient explosion and the loss of organizational details through residual connections between the encoder and decoder. Experimental results show that the root mean square error of the base matter image obtained by DM-Unet is as low as 0.041 g/cm³, the structural similarity reaches 0.9981, and the peak signal-to-noise ratio can reach 36.54 dB. Compared with traditional decomposition methods, DM-Unet shows better ability to restore organizational details, noise suppression, and edge information restoration, and is able to fulfill the task of DECT decomposition, which can provide accurate references for the subsequent medical diagnostic work.