A novel design of a two-stage nonlinear vibration isolation system, with each stage having a high-static-low-dynamic stiffness (HSLDS), is studied experimentally in this paper. The positive stiffness in each stage is realized by a metallic plate, and the corresponding negative stiffness is realized by a bistable carbon fiber–metal (CF) composite plate. An analytical model is developed as an aid to design a bistable composite plate with the required negative stiffness, and a static test of the plate is conducted to measure the actual stiffness of the plate. Dynamic tests of the two-stage isolator are carried out to determine the effectiveness of the isolator. Two tests are conducted, one with the bistable composite plates removed so that the isolator behaves as a linear device and one with the bistable composite plates fitted. An improvement in the isolator transmissibility of about 13 dB at frequencies greater than about 100 Hz is achieved when the bistable composite plates are added.