We consider a modified Chaplygin gas with the gravitational constant G and the cosmological constant A.The trivial solution describes decelerating phase to accelerating phase of the universe.The non-static with constant equation of state describes the inflationary solution.For static universe,G and A must be formed arbitrarily,and for static universe with constant equation of state,G and A should be constant.The Einstein field equation has two parameters,i.e.the gravitational constant G and the cosmological constant A.The Newtonian constant of gravitation G plays the role of a coupling constant between geometry and matter in the Einstein field equations.In an evolving Universe,it appears natural to look at this "constant" as a function of time.Numerous suggestions based on different arguments have been proposed in the past few decades in which G varies with time.[1,2] Dirac[3-6] proposed a theory with variable G motivated by the occurrence of large numbers discovered by Weyl,Eddington and Dirac himself.Many other extensions of Einsteins theory with time-dependent G have also been proposed to achieve a possible unification of gravitation and elementary particle physics or to incorporate Machs principle in general relativity.[7-9]