Different from traditional accelerometer, multi-threshold acceleration switch can be triggered to different working states by external accelerations without complex auxiliary circuits and controlling elements, which has great application potentials in aerospace, vehicle safety and consumer electronics. In this paper, a novel multi-threshold acceleration switch with anti-overloading function is designed and fabricated by incorporating both magnetic multi-stable structures and compliant cantilever contacts, which also can be used to distinguish specific acceleration pulse. To enhance the contact reliability, the magnetic compliant locking mechanism is introduced to prevent bouncing back phenomenon under overload acceleration. Considering the air-damping and multi-magnetic fields coupling effect, the dynamic design model is proposed for analyzing the nonlinear switch response. Then, threshold accelerations can be determined as ac1 = 3.78g, ac2 = 10.2g and ac3 = 6.95g in one direction while threshold accelerations in opposite direction are ac4 = 4.9g, ac5 = 8.47g and ac6 = 5.6g. The switch shows excellent threshold acceleration detection capability, and the inertial switch keeps open while the external acceleration is 0.2g less than the predefined threshold value. The experimental results show that the threshold acceleration with specific pulse width can be accurately identified, and the switch can bear strong overload acceleration comparing to traditional switches. Consequently, the proposed design method provides a new way for intelligent mechanical inertial sensors.