This paper presents maximum neural network algorithms for N-queen problems using the maximum neuron model. The maximum neuron model is proposed by Takefuji et al. in order to provide efficient neural network solutions for combinatorial optimization problems. In this model, one and only one neuron id always fired in each group of neurons, which can not only reduce the searching space drastically but also save the computation load. The simulation results show that the performance of our maximum neural network surpasses the existing neural network for the same problem. Particularly, the maximum neural network in shown to be much suitable for the semi-synchronous computation.