According to the basic optimisation principle of artificial neural networks, a novel kind of neural network model for solving the quadratic programming problem is presented. The methodology is based on the Lagrange multiplier theory in optimisation, and seeks to provide solutions satisfying the necessary conditions of optimality. The equilibrium point of the network satisfies the Kuhn–Tucker condition for the problem. The stability and convergency of the neural network is investigated, and the strategy of the neural optimisation is discussed. The feasibility of the neural network method is verified with the computation examples. Results of the simulation of the neural network to solve optimum problems are presented to illustrate the computational power of the neural network method.