This paper investigates a passive self-tuning piezoelectric energy harvester based on a beam-slider structure. The hardening nonlinearity is imparted to the system by two repulsive magnets to achieve broad bandwidth. The slider on the slightly tilted cantilever beam can automatically move along the beam to destabilize the low-energy orbit and track the high-energy orbit. The results of simulation and experiments show that the proposed design enables the nonlinear energy harvester to acquire a high energy converting efficiency and possess the anti-interference ability. In the frequency range of 21Hz-23Hz, the output power is enhanced by more than 25 times over the case with fixed mass at the free end. The tuning process is completely passive without any active actuators or sensors, which provides a promising method for designing an efficient nonlinear vibration energy harvester.