While wireless sensors, data transmission devices and medical implant devices tend to miniaturization and low consumption, energy supply modes such as batteries, solar energy and wind energy are limited due to their defects. Instead, vibration energy harvesting can open up new possibilities for self-supplying the low-consumption devices. The narrow-band random vibration with center frequency is a typical vibration in the environment, and its characteristics are closely related to the environment.This paper takes the energy harvesting system with bi-stable piezoelectric cantilever beam as a research object, and the characteristics of system's equivalent linear natural frequency, linear and nonlinear stiffness under different intervals between magnets are analyzed. By using the narrow-band random excitation with a certain bandwidth output of the bandpass filter to simulate environment vibration and using Runge-Kutta method to solve the system equation numerically, the response of system and the characteristics of energy harvesting are studied.It is observed that the variation of the magnet spacings at peak output voltage, which possesses a central frequency, is related to the variation of the equivalent linear natural frequency of the system with the interval between magnets. When the variation of magnet spacing is triggered by the narrow-band random excitation with a certain bandwidth, there is always a constant interval between magnets, making the system produce a peak output, which is like a bi-stable system that produces the peak output at optimal spacing under broad-band excitation. On the other hand, there are also more than one or two different magnet spacings making the system produce peak outputs while excitation's center frequency changes in a certain range, and the peak outputs are formed by bi-stable or single-stable “resonance” of the system, induced at the equivalent linear natural frequency. And the demarcation point spacing of the single-stable and bi-stable vibration of the system are the magnet spacing when linear stiffness is zero.Therefore, for the narrow-band random excitation in the actual environment, the magnet spacing of the energy harvesting system can be reasonably arranged according to the specific working conditions to achieve better electromechanical energy conversion. The findings in this paper can provide some theoretical and technical support for the study of harvesting the vibration energy with characteristics of narrow-band random excitation.