Abstract: For signal processing and process control, the minimax problem is a crucial point in research subjects. But efficient solutions to equality and inequality constrained nonlinear general minimax problems are relatively scarce. A minimax neural network model was proposed to solve the general minimax problem based on penalty function. In this model, the unique requirement is that the objective function and constraint functions should be first-order differentiable. In addition to the global stability analysis based on the Lyapunov function, the proposed model was simulated and its validity was evaluated with numerical results. Experimental results demonstrated that the proposed minimax neural network model can solve the problem in seconds which is more efficient than the conventional genetic algorithm and simplex genetic algorithms.