In the context of air traffic management (ATM), an accurate and reliable prediction of the aircraft’s trajectory is of critical importance. The enhanced predictability can decrease the chance of flight delays and can detect and reduce safety concerns as earlier stages. Aircraft trajectory prediction (TP) is stochastic in nature and many uncertainty factors will affect the final prediction results, such as weather uncertainties. A novel approach for probabilistic aircraft trajectory prediction is proposed using the Bayesian Neural Network in this paper. This approach has the capability of predicting the aircraft trajectory with the last on-file flight plan prior to takeoff including predictive uncertainties. It’s achieved by the use of dropout as Bayesian approximate Variational Inference (VI) in regular neural nets. The experiment is conducted with the Atlanta Air Route Traffic Control Center (ZTL) flight data and the corridor integrated weather system (CIWS) weather data from Sherlock Data Warehouse (SDW) on June 24th, 2019. The model is able to report a confidence interval (CI) of the prediction for both latitude and longitude coordinates. We notice that huge uncertainties still exist in the dataset which requires further investigation of other possible factors.