The power capability and maximum charge and discharge energy are key indicators for energy management systems, which can help the energy storage devices work in a suitable area and prevent them from over-charging and over-discharging. In this work, a model based power and energy assessment approach is proposed for the lithium-ion battery and supercapacitor hybrid system. The model framework of the lithium-ion battery and supercapacitor hybrid system is developed based on the equivalent circuit model, and the model parameters are identified by regression method. Explicit analyses of the power capability and maximum charge and discharge energy prediction with multiple constraints are elaborated. Subsequently, the extended Kalman filter is employed for on-board power capability and maximum charge and discharge energy prediction to overcome estimation error caused by system disturbance and sensor noise. The charge and discharge power capability, and the maximum charge and discharge energy are quantitatively assessed under both the dynamic stress test and the urban dynamometer driving schedule. The maximum charge and discharge energy prediction of the lithium-ion battery and supercapacitor hybrid system with different time scales are explored and discussed.