The (4+1)-dimensional cosmological model discussed in this paper is a direct product of the usual 4-dimensional spacetime and a. 1-dimensional compaetified internal space. The energy density of the 4-dimensional spacetime is supposed to be dominated by incoherent radiation and the energy-momentum tensor of the internal subspace is a step function. By solving the 5-dimensional Einstein field equations without cosmolog-ical term we get the de-Sitter solution to describe the usual spacetime and at a certain time it changes to the radiation-dominated solution for standard model, and the size of the internal subspace changes with time in a form of oscillation with amplitude attenuating and then contracts to a constant.