Abstract: The transformer isolated bi-directional DC/DC converter is the key component of the traction system in hybrid electrical vehicles(HEVs).We present a linear mathematic model of transformer isolated bi-directional DC/DC converter for HEVs based on the dual time scale theory and the state space average method.The approximate models are important especially for analysis and closed-loop control design of converter circuits. The differential equations, which govern the converter operation, change periodically among a set of linear differential equations because of the switch effect. Based on the time scale a state variable is decomposed into a fast-scale variable and a slow-scale variable. The fast-scale variable of leakage inductance is eliminated by substituting the fast-scale variable into slow-scale variable equations, resulting in reduced order differential equations. From this set of reduced order differential equations a completely averaged model of the isolated DC/DC converter is derived. The simulation results reveal that the circuit and mathematical model are well consistent.The averaged state variables can be treated as a small component plus a DC component, so the averaged variable can be decomposed into a dynamic small signal part and a DC part. This linear small signal model is suitable for control design and analysis at a steady point which is decided by the DC component. A PI controller is designed with this linear model.