Measuring and predicting atmospheric visibility is important scientific research that has practical significance for urban air pollution control and public transport safety. We propose a deep learning model that uses principal component analysis and a deep belief network (DBN) to effectively predict atmospheric visibility in short- and long-term sequences. First, using a visibility meter, particle spectrometer, and ground meteorological station data from 2016 to 2019, the principal component analysis method was adopted to determine the influence of atmospheric meteorological and environmental parameters on atmospheric visibility, and an input dataset applicable to atmospheric visibility prediction was constructed. On the basis of deep belief network theory, network structure parameters, including data preprocessing, the number of hidden layers, the number of nodes, and activation and weight functions, are simulated and analyzed. A deep belief network model suitable for atmospheric visibility prediction is established, where a double hidden layer is adopted with the node numbers 70 and 50, and the Z-score method is used for normalization processing with the tanh activation function and Adam optimizer. The average accuracy of atmospheric visibility prediction by the deep belief network reached 0.84, and the coefficient of determination reached 0.96; these results are significantly superior to those of the back propagation (BP) neural network and convolutional neural network (CNN), thus verifying the feasibility and effectiveness of the established deep belief network for predicting atmospheric visibility. Finally, a deep belief network model based on time series is used to predict the short- and long-term trends of atmospheric visibility. The results show that the model has good visibility prediction results within 3 days and has an accuracy rate of 0.79. Covering the visibility change evaluations of different weather conditions, the model demonstrates good practicability. The established deep learning network model provides an effective and feasible technical solution for the prediction of atmospheric meteorology and environmental parameters, which enjoys a wide range of application prospects in highway transportation, navigation, sea and air, meteorology, and environmental research.