Positron annihilation lifetime (PAL) measurements have been used to study the effect of branching (DB) and temperature on the atomic-scale free-volume properties and the structural transitions for hyperbranched polymer PEHO. According to the finite-term positron lifetime analysis and differential scanning calorimeter (DSC) measurements, the glass transition temperature was determined, which indicates that the higher the DB, the lower the glass transition temperature, and the higher the concentration of free-volume hole. Change in dispersion of the free volume shows that, with DB increase, there might be a disappearance of the dynamic heterogeneity in highly branched PEHO and a transition to homogeneous mass may take place. It is very interesting to observe the existence of two long-lived components (tau(3) and tau(4)) above T-g using the continuous lifetime analysis, which suggests that two kinds of different structures appear including a local ordered region and an amorphous region due to the molecular chains motion, indicating that an effective rearrangement of chains can take place, i.e., paracrystalline regions formed above T-g related to the packing density of chains.