There exists strong observational evidence for dark energy. The work done in this letter is just a new kind of extended modified gravity theory to yield a universe accelerating in time and dominated by dark energy. The extended modified gravity constructed here includes simultaneously a Gauss-Bonnet invariant term and a new Einstein-Hilbert term f (R, φ) = E(φ)R − μR −1 which depends on both the scalar curvature and on the scalar field φ through a generic function E(φ). It is shown that the presence of both terms provides remarkably many interesting features, which are discussed in some detail.The recent astronomical observations of the dynamics of galaxies, cluster of galaxies, Type SNeIa supernovae with redshift z > 0.35, cosmic microwave background (CMB) radiation and other cosmological observations suggest that our universe is spatially flat and currently undergoing a phase of accelerated expansion (Riess et al. , 2004Perlmutter et al. 1999;Schmidt et al. 1998;Steinhardt et al. 1999;Persic et al. 1996;Cunha 2009). However, nearly three quart of the universe consists of dark energy with negative pressure and negative equation of state parameter −1.14 < w < −0.93 at 68% confidence level, dubbed dark energy (DE), whose nature is still a source of much debate among high energy physicists and cosmologists. Regardless of the theoretical difficulties in understanding the speculative nature A.R. El-Nabulsi ( ) of DE, independent observational evidence for its existence is remarkably robust. Explanations have been sought within a wide range of physical phenomena, including the cosmological constant, exotic fields such as a Brans-Dicke scalar field (Brans and Dicke 1961), phantoms and quintessence, K-essence, viscous fluid, Chaplygin gas and Generalized Chaplygin, holographic dark energy and so on (El-Nabulsi 2008a, 2009a, 2009b, 2010a, 2010bSetare 2006aSetare , 2007 Saridakis 2008a, 2008b). More recent DE models include the one containing a negative kinetic scalar field and a normal scalar field , or a single scalar field model (Li et al. 2005) and interacting holographic dark energy models (Wang et al. 2006). These cosmological models were constricted in order to gain insight into the occurrence of the transition of the dark energy equation of state and the mechanism behind this transition. Most of these phenomenological attempts are accompanied by embarrassing problems and we still ignore which of these models are the most viable. We are in reality encountered with many enigmas and theoretically unsolved problems, in particular the cosmological constant, and the cosmic coincidence and fine-tuning problems. Another serious issue concerns the addressed question: " why the universe started to accelerate very soon after the completion of the formation of galaxies and clusters of galaxies even if a positive cosmological constant is present ".On the other side, scalar-tensor gravity theories have been widely applied in modern cosmology since the pioneering work of Brans and Dicke several decades ago. However, it has been ...