Journal of Electronic Systems Cuiping Li 8 2 2018 10.6025/jes/2018/8/2/57-71 http://www.dline.info/jes/fulltext/v8n2/jesv8n2_2.pdf In this paper, I design a new neural network for solving least absolute deviation problems with equality and box constraints. Compared with some existing models, the proposed neural network needs the fewest state variables and has only one-layer structure. By constructed a proper Lyapunov function, the following two results can be proved. First, it is stable in the sense of Lyapunov. Second, the solution of the proposed model can converge to an exact optimal solution of the problem. Finally, its validity and transient behaviors are demonstrated by some simulation results.