The invention relates to a multi-stable nonlinear energy well with a piecewise linear beam and permanent magnet negative stiffness. The multi-stable nonlinear energy well comprises the piecewise linear beam which is composed of three piecewise linear rods with different stiffness. One end of the piecewise linear beam is fixed to a piecewise linear beam pedestal, and the other end of the piecewiselinear beam is inserted into an MNES mass block. During installation, a certain pre-compression amount is reserved between the piecewise linear rods of the two sides and the MNES mass block. A gap isreserved between the piecewise linear rod in the middle and the MNES mass block. Along with up-and-down movement of the MNES mass block, the compression amount between the MNES mass block and the piecewise linear beam is changed, and piecewise linear positive stiffness is produced. The required negative stiffness is produced through inner magnets and outer magnets, and required multiple stable positions are constructed through the optimal cooperation of the positive stiffness and negative stiffness. Vibration energy of a to-be-damped system is transmitted into the energy well in a unidirectional mode, and finally the energy is rapidly dissipated through damping by the energy well, and thus main system vibrations can be efficiently restrained. The energy well is simple in structure, wide invibration suppressing frequency band and remarkable in vibration suppressing effect.