Sparse-view computed tomography (CT) is one of the main means to reduce radiation risk. When the projection data is highly undersampled, the reconstructed CT image may suffer from serious stripe artifacts and structural information loss. In this paper, we propose a sparse-view CT reconstruction network architecture combining mixed attention (MA) and an iterative reconstruction strategy, called MAIR-Net. Firstly, the approach expands the proximal gradient descent into the neural network and uses an initial value enhancement module between the gradient descent module and the proximal mapping module. The aim is to enhance the flow of detailed information between different layers, fully retain image details, and improve the network convergence speed. Secondly, the mixed attention module (MAM) is introduced into the reconstruction process as a regularization term. It adaptively fuses local and non-local features of the image, which are used to reduce the over-smoothing of the reconstructed image and fully retain the details of the reconstructed image, respectively. Experimental results showed that the proposed method can better retain the details of the reconstructed image and improve the quality of the reconstructed image while inhibiting the sparse angle artifacts of the CT reconstructed image.