Abstract: In order to verify the existence and global stability of positive periodic solutions to the food chain system of three species with time delays in a periodic environment, this article constructed a suitable Lyapunov function to obtain a set of sufficient conditions for the global stability of the system by using Gaines and Mawhin's continuation theorem of coincidence degree theory. The author considered three species (y₁, y₂, y₃; y₁ is the prey to y₂; y₂ is the prey to y₃), growth rate (of y₁ primarily) and mortality rate (of y₂ and y₃ primarily) of independently existed species, as well as the interspecies pillage and sustentation capabilities. The prior bounds should be estimated for three species separately; furthermore, the upper and lower bonds should be estimated more accurately.