In recent years, SLAMMOT (simultaneous localization, mapping and moving object tracking) has attracted widespread attention in the mobile robot field. This paper proposes a new approach, SLAMMOT-SP, which combines SLAMMOT and scene prediction (SP). It extends the SLAMMOT problem to simultaneous map prediction and moving object trajectory prediction. The robot not only passively collects the data and executes SLAMMOT, but actively predicts the scene. The recursive Bayesian formulation of SLAMMOT-SP is derived for real-time operations. A generalized framework for tracking and predicting the moving objects is also proposed. Simulations and experiments show that the proposed SLAMMOT-SP is effective and can be performed in real-time.