The present universe is dominated by repulsive dark energy. It is natural that the coupling between the dark energy and the attractive gravity has to be taken into account in studying the evolution of our universe. Here, we induce an evolution equation for dark energy-dark matter-coupled universe. The solutions of the dynamic equation provide a specific picture of cosmic evolution, which is well compatible with current observed evolution histories of both Hubble parameter and equation of state parameter of dark energy. In this picture, the already observed universe has undergone through three epochs-the epoch of equilibrium between gravity and dark energy at cosmological redshifts , the phase transition epoch at z between about 0.5 and 1, and the present acceleration epoch starting from . The expected matter-dominated deceleration epoch has not been seen yet, which requires future deep observations to look back upon more early universe.