In this study, a vibration energy-harvesting system is developed by first proposing a horizontal bi-stable vibration model comprising an elastic spring and a mass block and then applying an electromagnetic induction power generation device composed of a magnet and a coil. Subsequently, based on a weight function that considers the mutual positional relationship between the magnet and conducting coil, a set of simultaneous governing equations that consider the elastic force of the elastic spring and the Lorentz force of electromagnetic induction is derived. Additionally, a numerical analysis method employing the Runge–Kutta method is utilized to obtain a numerical solution for the vibration response displacement and vibration power generation voltage simultaneously. Experiments are performed to verify the results yielded by the proposed bi-stable vibration energy-harvesting system. The results shows that the measured vibration response displacement and the vibration power generation voltage are consistent with the analytical results. Moreover, issues including the identification of damping coefficients that consider the mutual effects of normal kinetic friction and electromagnetic induction damping forces, as well as the effects of electromagnetic induction damping on the vibration response displacement, are discussed comprehensively. Simultaneously adding random and periodic signals to the bi-stable vibration model results in stochastic resonance and improves both the vibration amplification effect and vibration power generation.