Abstract: In this paper, after a brief discussion on the theory of EM-wave propagation velocity, we describe the history of contradiction between the relativity and the quantum mechanics,thus we give a theoretical basis of researches on the waves with its velocity beyond that of the light. Then mathematical and analytical studies on the quantum tunneling effect are presented. An experiment on visible light faster than c is described. The significant result of waveguide's quantum tunnel theory is presented,and on this theoretical basis,an evanescent-mode barrier has been designed which was used for the experiment of microwaves faster than light.