Abstract: Abstract: Vibration energy harvesting systems can convert the vibrational energy into the useful electric power, thereby offer a promising source of renewable energy for sustainable development of a society. However, there remains a great challenge on high power density and broadband energy collection under random power spectrum. In this study, a high power-density and broadband Magnetic-Floating Energy Harvester (MFEH) was presented for diverse vibration excitations. A COMSOL Multiphysics software was used to calculate the relationship between magnetic restoring force and displacement during the vibration. A mathematical model was established to explore the effects of different parameters on the performance of energy harvester, according to the governing equations of magnetic-floating vibration system and Kirchoff's law. The simulation results show that the maximum output voltage varied slightly from 16 to 22 V, as the mass of levitated magnet increased, indicating that the variation in mass can pose some influence on the maximum output voltage. Nevertheless, the resonant frequency decreased, when the mass of levitated magnet increased. The excitation acceleration has a significant influence on the maximum output voltage, whereas, there was a relatively small increase in the resonant frequency. Specifically, the spacing, d0, has a significant impact on the curve shape of output voltage. There was only a unique solution for the governing equation, when the values of d0 were 53 and 52 mm, respectively, where the curves of output voltage were stable. But the solution for the governing equation was not unique, when the d0 was less than 52 mm. Consequently, the curve included the stable and unstable solutions, indicating that the jump phenomenon occurred in this case. Analogous to the parameter spacing d0, the damping ratio also strongly determined the curve shape. When the damping ratio was less than 0.21, the curve also included the stable and unstable solution in presence of the jump phenomenon. Diverse excitation conditions, such as the sinusoidal sweeping and fixed frequency vibration, were selected to verify the capacity of power generation. Subsequently, the performance of energy harvester was evaluated by the indexes of efficiency, effectiveness, and the volume figure of merit. A regulated power supply circuit was also designed, combined with the practical application. A mathematical model of random excitation was established, according to the spectrum characteristics for a random road, when an agricultural machine working on hilly and mountainous areas. The solution of stationary probability density was obtained using the Fokker-Planck-Kolmogorov (FFK) equation expression for the response amplitude of probability density function. Experimental results showed the maximum output voltage ranged from 5.92 to 21.52 V, as the excitation frequency varied from 9.77 to 31.75 Hz under diverse amplitude. The maximum power reached 81.93 mW at 10 Hz. From 5 Hz to 50 Hz, the maximum deliverable power is 81.93 mW. The efficiency, effectiveness, and the volume figure of merit for the designed energy harvester were 2.85%, 9.85% and 39.74%, respectively. Five peaks can be obtained for the power spectral density of output generating voltage in energy harvester, where the frequencies were 9.80, 29.41, 36.76, 36.76, 51.47, and 71.08 Hz, indicating a broadband power response. The proposed device can be applied for powering the most sensors of agricultural machinery and equipment in hilly and mountainous areas.