Based on the stiffness theory of wave spring, this paper proposes the wave springs made of glass fiber reinforced plastic (GFRP) and investigates the effect of the number of periods on the GFRP wave springs’ stiffness and frequency response characteristics. First of all, five different periods of composite wave springs which have identical outside dimensions are designed. Afterwards, the load-displacement curves of the GFRP wave springs are obtained using a combination of experimental and finite element analysis (FEA). Finally, the frequency response characteristics of the GFRP wave springs are measured using a force hammer excitation, and the experiment results of a GFRP wave spring are compared with a metal helical spring. The results show that the stiffness of the GFRP wave spring decreases from 34.84 N/mm to 20.59 N/mm with the increase in the number of periods. As the number of periods increases, the vibration attenuation increases from 16.32 dB to 69.17 dB. The stiffness of the GFRP wave spring is increased by 90.30% and the weight is reduced by 26.78%. The vibration isolation interval and vibration attenuation amplitude of the GFRP wave spring are higher than the metal helical spring.