A new modified-gravity theory, referred to as the unified electro-gravity (UEG) theory, has been recently proposed. The theory introduces a new gravitational field in the presence of an electromagnetic field or radiation, while maintaining the conventional Einstein-Newtonian gravity in the external region of an electrically neutral, non-radiating body. The new UEG theory has been successfully applied to self-consistently model a spinning electron. The UEG theory, successfully applied as a substitute for the hypothetical “dark-matter” in spiral galaxies and galaxy clusters, were presented in recent AAS conferences. In this paper, we would extend the UEG theory to model the observed accelerated expansion of the universe, without need for any hypothetical “dark-energy” or “dark-matter.” The new UEG acceleration, produced in proportion to the cosmic background radiation-density, maybe modeled as an equivalent mass distribution over the observable universe, in addition to distribution of the conventional baryonic mass. The velocity of expansion of the current universe is found to be significantly in excess of what can be supported by the total mass (conventional baryonic, plus the new UEG equivalent-mass). It is assumed that the excess velocity would be supported by UEG acceleration due to any future star lights. In this presentation, we will focus on the UEG theory to explain the accelerated expansion in the current and recent past of the universe. As the universe expands, the equivalent mass due to the new UEG effect, enclosed in a co-moving volume, would reduce, while the enclosed baryonic mass remains constant. The reduction of the total mass would lead to an increase of the excess velocity as the universe expands, in order to conserve kinetic energy associated with the excess velocity, enforced as a requirement in the new UEG cosmology. This would result in a net acceleration of the expansion, in the current and recent past of the universe (z<1). However, in sufficient past (z>1), the normal gravitational deceleration (inward acceleration) supported by the total mass would be larger than any accelerated expansion due to the excess velocity, leading to a net deceleration of the universe’s expansion for z>1. Results from the UEG cosmology compare well with the standard model using the hypothetical dark-matter and dark-energy, in agreement with measurements of high-z supernovae and gamma-ray bursts.