Accurate forecasting of short-term photovoltaic power output is vital for enhancing the operation efficiency of photovoltaic (PV) power stations and ensuring the safety and stable operation of grid-connected PV plants. Therefore, a short-term power forecasting model based on a backpropagation neural network with atom search optimization optimizes the weights and thresholds. Meanwhile, the Pearson correlation coefficient formula is introduced to screen the key meteorological factors and eliminate redundant factors, i.e., total irradiance, temperature, humidity, and direct irradiance are taken as the input of the prediction model. Moreover, the Euclidean distance formula is used to establish a customized training set for each test data which improves the dependability of the training set. Lastly, with the simulations of actual data from a solar farm in Yunnan, China, it is verified that the proposed ASO-BPNN model is competent to forecast the PV power generation.