A closed model of the universe was constructed according to the assumption that very minor fraction of the dark energy transfers so slowly to matter and radiation. The cosmological parameter is no longer fixed but represents so slowly decreasing function with time. In this model the universe expands to maximum limit at t_me = 26.81253 Gyr, then it will contract to a big crunch at t_bc = 53.6251 Gyr. Observational tests to the closed cosmic model were illustrated. Distributions of the universe expansion and contraction speed established in this model which indicated that the expansion speed in the early universe is appreciably high, then it will decrease rapidly until it vanishes at t_me. However, the contraction speed of the universe increases continuously until the time just before t_be. Distributions of the universe expansion and contraction acceleration were performed empirically which confirmed the previous result were performed empirically. In the closed cosmic model the universe history can be categorized into six main stages, these are the first radiation epoch, the first matter epoch, the first dark energy epoch, the last dark energy epoch, the last matter epoch and the last radiation epoch. Distributions of the density parameters of the radiation, matter, dark energy and the total density as well as the distributions of temperature of the radiation and non-relativistic matter were all investigated in this model at all epochs of the universe.