The article states a problem of a multiclass network classification of computer attacks. To solve it, the authors consider an option of applying deep neural networks. For this research, the authors selected the architecture of a deep neural network based on the strategy combining a set of convolution and recurrent LSTM layers. The research suggests optimizing the neural network parameters on the basis of a genetic algorithm. The authors present the simulation results that show an opportunity to solve the task of network classification in real time.