PM_2.5 is an important indicator for measuring the concentration of air pollutants, and monitoring and predicting its concentration can effectively protect the atmospheric environment and further reduce the harm caused by air pollution. As automatic air quality monitoring stations are constructed on a large scale, the air quality prediction model built by traditional machine learning can no longer meet the current needs. This study proposes a Gaussian-attention prediction model based on the multi-head attention mechanism and Gaussian probability estimation and utilizes the data from a monitoring station in Shenyang for training and tests. Because PM_2.5 concentration is affected by other air quality data, this model uses the information alignment of hierarchical time stamps (week, day, and hour) of air quality data as input and extracts the time-series correlation features of different subspaces with the multi-head attention mechanism. More complete and effective feature information is thereby obtained, and prediction results are then acquired by Gaussian likelihood estimation. A comparison with multiple benchmark models is conducted, and the mean squared error (MSE) and mean absolute error (MAE) of the proposed Gaussian-attention prediction model are respectively 21% and 15% lower than that of the DeepAR model. Effectively improving prediction accuracy, the proposed model can accurately predict PM_2.5 concentration.