This paper presents a chaotic neural network (CNN) model through adding chaotic control quantities to each neuron. The chaotic control quantities are used to control the neural network energy function increasing, decreasing or keeping unchanged which can help the neural network to enlarge searching space to get optimal solutions and avoid local minima or invalid solutions. In order to study the delay bound and the least cost multicast routing problem, a new algorithm based on CNN is proposed to optimize the multicast tree with delay bound, and the energy function is defined to represent the cost of optimal path with the delay bound. Through the comparative simulation with other algorithms, the results show that the proposed algorithm is both efficient and feasible in constructing the optimal delay bound multicast tree.