This paper studies the system modeling and mode-switch control for a novel 3-mode (serial/parallel/pure electric) range-extender electric vehicle (REEV). The REEV is modeled with low-order dynamics of 8 subsystems: the driving pattern, driver's behavior, lithium batteries, a spark-ignition engine, a traction motor, a generator, a 6-speed transmission, and a longitudinal vehicle dynamics. Dynamics of the REEV is the integration of above subsystems. To properly evaluate the system performance of the REEV, a rule-based mode-switch control rule is designed with 7 operation modes (System Ready, EV, Serial, Coast Down, Coast-Down Regen., Idle Regen., Parallel). By applying the control rules for the 3-mode REEV, the vehicle can properly operate. Simulation is conducted on the Matlab/Simulink platform. The results show that this study details the system dynamics of subsystems and the vehicle. Meanwhile the rule-based control strategy governs the subsystems well. The developed simulator can be utilized for specification designs of real vehicles and for vehicle control unit designs in the near future.