The identification of copy number variations (CNVs) helps the diagnosis of many diseases. One major hurdle in the path of CNVs discovery is that the boundaries of normal and aberrant regions cannot be distinguished from the raw data, since various types of noise contaminate them. To tackle this challenge, the total variation regularization is mostly used in the optimization problems to approximate the noise-free data from corrupted observations. The minimization using such regularization is challenging to deal with since it is non-differentiable. In this paper, we propose a projection neural network to solve the non-smooth problem. The proposed neural network has a simple one-layer structure and is theoretically assured to have the global exponential convergence to the solution of the total variation-regularized problem. The experiments on several real and simulated datasets illustrate the reasonable performance of the proposed neural network and show that its performance is comparable with those of more sophisticated algorithms.