An urban sound event classification model based on the N-order Dense Convolutional Network (abbreviated to N-DenseNet) is proposed for the problems of insufficient classification accuracy and generalization ability of existing models. First, the network structure of the DenseNet is briefly introduced. Then, dense connection in the DenseNet is improved by N-order state-dependent connection based on the N-order Markov model. Furthermore, combining advantages of both the DenseNet and N-order Markov, a novel network architecture, i.e., the N-DenseNet, is proposed in this paper. Theoretically, the N-DenseNet satisfying the premise of alleviating vanishing-gradient, can not only produce efficient integration of feature information from the layers, but also accelerate the convergence speed. Finally, in order to validate advantages of the new model, 1-DenseNet and 2-DenseNet are respectively exploited in the urban sound event classification based on the UrbanSound8K and Dcase2016 dataset. Experimental results show that the accuracy of the two above-mentioned models is respectively 83.63% and 81.03%, which also demonstrates a higher classification accuracy and a better generalization performance of the N-DenseNet.