In rotational electromagnetic generator based vibration energy-harvesting systems, the generator rotor is an inerter. From analysis, it is found that the inerter decreases system frequency bandwidth in single-degree-of-freedom (SDOF) energy-harvesting systems. The maximum electric power output of a SDOF system is limited by mechanical damping and maximum stroke that allowed. Two-degree-of-freedom (2DOF) energy-harvesting systems was proposed in recent years and has been shown to have the potential to have better power, power/stroke ratio, and frequency bandwidth performance compared with SDOF systems. However, extra mass has to be added in most of the case. In this paper, a new design of inerter-based-2DOF energy-harvesting system was proposed by adding a spring in series with the inerter in SDOF system. No extra mass is added compared with its counterpart SDOF system. Optimal specific power at limited stroke were obtained by tuning system parameters, which includes resonance frequency ratio, spring ratio, mass ratio, and damping ratio. The contribution of each parameter to system performance was analyzed. The results show that the proposed inerter-based-2DOF system has better performance compared with the SDOF system. The inerter-based-2DOF can have larger specific power and larger power/stroke ratio over a wider frequency bandwidth. Simulation also show that improved performance not only obtained with sinusoidal excitation with constant displacement amplitude, but also with sinusoidal excitation with constant force amplitude.