Bundle adjustment (BA) is the major optimization step simultaneously refining 3D coordinates and accounts for a large portion of execution time in visual simultaneous localization and mapping (SLAM). While the Levenberg-Marquardt (LM) based algorithms have been commonly used for fast BA, recent solutions adopting iterative and originally slow Gaussian belief propagation (GBP) show its potential to be fast and accurate on emerging computation platforms. We propose a novel architecture to predict the message passing in GBP with deep neural networks. The model generates messages several iterations ahead to significantly reduce the number of required computation loops. Also, the process converges with hyperparameter tuning and avoids the dependency of an arbitrary damping factor for GBP to be stabilized. Compared with standard GBP, the learning-based approach achieves the same level of accuracy while running 17.7 times faster under GPU acceleration.