In this Meter paper we study a predator-prey system, modeling the interaction of two species with diffusion and T-periodic environmental parameters.It is a Leslie-Gower type predator-prey model with Holling-type-II functional response.We establish some sufficient conditions for the ultimate boundedness of solutions and permanence of this Swivel Lounge Chair with Cushion (set of 2) system.By constructing an appropriate auxiliary function, the conditions for the existence of a unique globally stable positive periodic solution are also obtained.Numerical simulations are presented to illustrate the results.