The constrained L1 estimation is an attractive alternative to both the unconstrained L1 estimation and the least square estimation. In this letter, we propose a cooperative recurrent neural network (CRNN) for solving L1 estimation problems with general linear constraints. The proposed CRNN model combines four individual neural network models automatically and is suitable for parallel implementation. As a special case, the proposed CRNN includes two existing neural networks for solving unconstrained and constrained L1 estimation problems, respectively. Unlike existing neural networks, with penalty parameters, for solving the constrained L1 estimation problem, the proposed CRNN is guaranteed to converge globally to the exact optimal solution without any additional condition. Compared with conventional numerical algorithms, the proposed CRNN has a low computational complexity and can deal with the L1 estimation problem with degeneracy. Several applied examples show that the proposed CRNN can obtain more accurate estimates than several existing algorithms.