A simplified neural network model is proposed to solve a class of linear matrix inequality problems. The stability and solvability of the proposed neural network are analyzed and discussed theoretically. In comparison with the previous neural network models (Lin and Huang, Neural Process Lett 11:153–169, 2000; Lin et al., IEEE Trans Neural Netw 11:1078–1092, 2000), the simplified one is composed of two layers rather than three layers, and the neuron array in each layer is triangular rather than square. The proposed approach can therefore reduce the complexity of the neural network architecture. In addition, the simplified neural network can also be extended to solve multiple linear matrix inequalities with specific constraints, which enlarges the application domain of the proposed approach. Finally, examples are given to illustrate the effectiveness and efficiency of the simplified neural network.