Vibrational energy harvesting systems with linear electromechanical generators have been largely studied, due to their simple structures and convenience in application. However, the ambient vibration characteristics such as random, time-varying or low-frequency properties make the linear electromagnetic devices cannot be excited at their resonances, which will greatly affect the energy harvesting efficiency. Some attempts to improve the efficiency of a vibration energy harvesting system involve both expand the operating bandwidth and enlarging the magnitude of power output. To this end, a scissor-like energy harvesting system with equivalent nonlinear damping and linear stiffness has been developed in this study. It has been shown that, due to the beneficial nonlinear damping effects provided by the scissor-like structure, the proposed system can greatly improve the vibration energy harvesting performance in terms of the magnitude of power output and energy harvesting bandwidth. On the other hand, the structure parameters of the proposed system can be modified to achieve more significant energy harvesting performance. Moreover, to achieve tunable resonant frequency of the energy harvesting system, the scissor-like structure has been updated by attaching a new lever-type system. In this way, the energy harvesting performance can be improved by tuning the proposed system according to the properties of the surrounding vibration sources. In this paper, both harmonic and random excitations have been adopted to verify the performance of the proposed energy harvesting system.