Several recent investigations have shown that there is a holographic relationship between the bulk degrees of freedom and the surface degrees of freedom in the spacetime. Furthermore, the entropy on the horizon can produce an entropic force effect on the bulk degrees of freedom. In this paper, we explore the dynamic evolution law of the universe based on the idea of the entropic force and asymptotically holographic equipartition and further analyze the thermodynamic properties of the current model. We get the age of the universe, the relation between the luminosity distance and the redshift factor and the deceleration parameter which are consistent with astronomical observations. In addition, we can well explain the age of the universe and the mechanism of accelerated expansion without introducing dark energy for the evolution history of the universe up to now. We also show that the generalized second law of thermodynamics, the energy balance condition and the energy equipartition relation always hold. More importantly, the energy balance condition is indeed a holographic relation between the bulk degrees of freedom and the surface degrees of freedom of the spacetime. Finally, we analyze the energy conditions and show that the strong energy condition is always violated and the weak energy condition is satisfied when $tleq2t_{0}$ in which $t$ is the time parameter and $t_{0}$ is the age of the universe.
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