Competing species can coexist or not is a central problem in biological problems. In previous work, we can find that two strongly competing species cannot coexist but for three species, it is possible for them to coexist. However, due to the lack of maximum principle, it is difficult to find the stationary solutions. In this talk we want to study the existence and stability of the non-monotone traveling wave solutions of the three-species systems which can be used to construct coexistence pattern numerically. Under the concept from competition-mediated coexistence, we suppose that there are two species U and V compete strongly with each other in a system, and the third species W invades into the system of U and V. We focus on the case that the competition rates from W on U and V are small enough, then by the super-sub-solution techniques, exact solutions and the heteroclinic bifurcation theory, we can prove the existence of the solutions. Finally we also prove stability by the spectral analysis of the linearized operators. This is a joint work with Chiun-Chuan Chen, Li-Chang Hung, Masayasu Mimura and Toshiyuki Ogawa.​