Recent astrophysical measurements strongly suggest the existence of a missing energy component dubbed dark energy that is responsible for the current accelerated expansion of the universe. A new class of modified gravity theory is introduced which yields a universe accelerating in time and dominated by dark energy. The new modified gravity model constructed here concurrently includes a Gauss-Bonnet invariant term, barotropic fluid with a time-dependent equation of state parameter,a Coleman-Weinberg (CW) potential-like expression V(O)=ξφm In φn and a new Einstein-Hilbert term f (R, φ)＝E(φ)R which depends on both the scalar curvature and the scalar field 0 through a generic logarithmic function E(φ)＝In 0. Here m and n take different values from the standard CW potential and ξ is a real parameter.It was shown that the presence of these terms provides many useful features which are discussed in some detail.