Abstract: 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 orbits of equal size. We classify all cubic bi-Cayley graphs over a nonabelian group of order 3p(p is odd prime). We prove that the cubic vertex-transitive bi-Cayley graphs must be isomorphic to Cayley graphs. In addition, the automorphism group of the graph is discussed.