Abstract: Learned iterative soft-thresholding algorithm (LISTA) expands the iterative soft-thresholding algorithm (ISTA) into a recursive feedforward neural network to optimize the solution of sparse recovery. To address the problem that each iteration in LISTA only relies on the previous iteration point resulting in the limitation of convergence rate, this paper proposes a learned soft-thresholding algorithm with multi-state memory mechanism (LISTA-MM). This method improves LISTA based on the first-order iterative fixed-step algorithm and sets the state connection degree. This algorithm selectively combines the sparse information of several previous iteration points, ensures that the sparse information is transferred correctly and fully utilized during the iteration, and thus speeds up the convergence speed of the algorithm. The experimental results show that LISTA-MM not only ensures the precision of sparse recovery, but also effectively improves the convergence rate of sparse recovery. In addition, this paper extends LISTA-MM into a convolution manner and explores its application in image super-resolution. The experimental results show that the LISTA-MM based network is superior to other networks in both image quality evaluation and visualization effect, and the reconstructed images have clear and detail texture closing to the original image.