Aiming at the problem of sparse signal reconstruction, an optimization algorithm based on Recurrent Neural Network (RNN) was proposed. Firstly, the signal sparseness was represented, and the mathematical model was transformed into an optimization problem. Then, based on the fact that the l ₀-norm is a non-convex and non-differentiable function, and the optimization problem is NP-hard, under the premise that the measurement matrix A met Restricted Isometry Property (RIP), the equivalent optimization problem was proposed. Finally, the corresponding Hopfield RNN model was established to solve the equivalent optimization problem, so as to reconstruct sparse signals. The experimental results show that under different observation number m, compared the RNN algorithm and the other three algorithms, it is found that the relative error of the RNN algorithm is smaller and the observations number is smaller, and the RNN algorithm can reconstruct the sparse signals efficiently.