By analyzing the dynamic behaviors of the transiently chaotic neural network and greedy heuristic for the maximum independent set (MIS) problem, we present an improved transiently chaotic neural network for the MIS problem in this paper. Extensive simulations are performed and the results show that this proposed transiently chaotic neural network can yield better solutions to p-random graphs than other existing algorithms. The efficiency of the new model is also confirmed by the results on the complement graphs of some DIMACS clique instances in the second DIMACS challenge. Moreover, the improved model uses fewer steps to converge to stable state in comparison with the original transiently chaotic neural network.