In view of solving linear programming problems with parameters both in objective function and constraints, a computational method based on novel smooth exact penalty function neural networks is proposed. First, the error function is introduced to constructing the approximate function of unit step function, which is used to give the smooth penalty function that more accurately approximates the L1 exact penalty function, and its basic properties are discussed. Second, the neural network model for parameter linear programming problems is constructed based on the proposed smooth exact penalty function and the stability and convergence of the neural networks are proved. Moreover, the specific calculation steps of our proposed neural network model for the optimization are given. Finally, a numerical example is given to illustrate that the proposed method possesses the smaller penalty factor, easier construction and higher accuracy.