A graph is said to be a Bi-Cayley graph over a group $H$ if it admits $H$ as a semiregular automorphism group with two vertex-orbits. The study about the symmetry of  Bi-Cayley graph is an important topic in algebra graph. Using the structure of the cubic tetracirculant graph,  we study cubic connected edge-transitive bi-Cayley graphs over semidihedral groups  and give  a classification of this kind of graphs.