Positron annihilation lifetime spectroscopy has been used to study the free volume properties of the cross-linked polyurethane network as a function of temperature in the range from 15K to 300K. The glass transition of polyurethane was observed and the thermal expansion coefficient of the free volume was calculated. Analysis of the ortho-positronium (o-Ps) lifetime distribution shows that the distribution of the free volume in polyurethane is slightly broadened with the increasing temperature in the glassy state, and then significantly broadened with the increasing temperature above the glass transition.