Train running safety is considered one of the key criteria for advanced highway trains and bogies. While a number of existing research studies have focused on its measurement and monitoring, this study proposes a new and effective train running a safety prediction framework. The wheel derail coefficient, wheel rate of load reduction, and wheel lateral pressure are considered the decision variables for the safety framework. Data for actual measured rail conditions and vibration-based signals are used as the input data. However, advanced trains and bogies are influenced more by their inertial structures and mechanisms than by railway conditions and external environments. In order to reflect their inertial influences, past data of output variables are used as recurrent data. The proposed framework shares advantages of a general deep neural network and a recurrent neural network. To prove the effectiveness of the proposed hybrid deep-learning framework, numerical analyses using an actual measured train-railway model and transit simulation are conducted and compared with the existing deep learning architectures.