A real-time vehicle dynamics model is an essential component for Hardware-in-the loop and Operator-in-the loop simulations. For the real-time vehicle dynamics analysis, solution stability is rather important than the solution accuracy. Thus, it is necessary to apply implicit integrators to the real-time vehicle model for the stable solution. In this paper, HHT- α implicit integration method has been applied. For real-time analyses require the same amount of computational time for each integration step, an integration method which does not require iterative procedure was developed through the linearization procedure of the equations of motion. The proposed method is applied to the trailing arm type suspension subsystem in order to verify the effectiveness of the method.