The existence of traveling wave solutions for two species Lotka-Volterra competitive system with delays was investigated.Based on the theory of the existence of traveling wave solutions for reaction-diffusion systems with delays, the main problem was transfered to look for a pair of upper and lower solutions for the system.And the asymptotic behavior of the system was given as an attenuated motion tending to the infinity.The study makes up and improves the results of the existence of traveling wave solutions of a class of systems.