Broadcast ephemeris errors are one of the key factors affecting the positioning accuracy of non-augmented Beidou airborne navigation receivers. To improve the navigation and positioning precision of non-SBAS (Satellite-Based Augmentation System) augmented airborne satellite navigation receivers and reduce broadcast ephemeris errors during the solution process, we propose a hybrid prediction model for broadcast ephemeris errors. Using precise ephemeris data as a reference, we calculate the broadcast ephemeris errors of Beidou B1I/B3I signals. The variational mode decomposition (VMD) method is employed to decompose the Beidou satellite orbit errors into multi-dimensional errors with time markers. The whale optimization algorithm (WOA) is utilized to optimize the number of decompositions and the penalty factor, using the minimum envelope entropy of the decomposed error signals as the optimization criterion. These sequences are then input into a bidirectional long short-term memory (Bi-LSTM) network to capture temporal correlations within the data. A ground-based hybrid prediction model for broadcast ephemeris errors is constructed to calculate correction values for the broadcast ephemeris orbit errors in real time. By leveraging the Regional Short Message Communication function, the error corrections are transmitted to the Beidou airborne receiver, where error compensation is performed during navigation and positioning calculations to correct the broadcast ephemeris orbit errors. Simulation results indicate that, compared to traditional machine learning and Bi-LSTM network algorithms, this method reduces the RMSE (Root Mean Square Error) of the predicted broadcast ephemeris orbit errors by 81.43% and 70.17%, respectively.