Neural network based on back-propagation (BP) algorithm is a widely used prediction model. However, the nodes number of the first hidden layer, the learning rate and momentum factor are usually determined manually, which affects the forecast accuracy of network. Therefore, in this paper, to improve the forecast accuracy, firstly, the nodes number of the first hidden layer is selected adaptively based on minimizing mean square error (MSE). Secondly, improved genetic algorithm (GA) is proposed to train the learning rate and momentum factor dynamically, which includes multi-point crossover and single point mutation. Thirdly, we construct a new neural network model based on the adaptively selected nodes number of the first hidden layer, the dynamically selected learning rate and momentum factor, which is called HN-GA-BP neural network model. Finally, the proposed neural network model is used to forecast the carbon dioxide contents in China for fifty years. Experimental results demonstrate the effectiveness of the proposed HN-GA-BP neural network model.