The structure, magnetic and electric properties of Sr2FeMoO6 (the as-made sample) and samples after heat treatment were investigated. The nuclear and magnetic structures of the samples were studied using neutron powder diffraction at room temperature.The results show that the tunneling magnetoresistance of polycrystalline Sr2FeMoO6 depends on its annealing temperature. Annealing at 800 ℃ makes the minimal magnetoresistance(MR) elevated, which may be due to the change of the grain size or the modified intergranular connections. Because of the impurity phase of Fe which probably affects the magnetotransport properties is much larger in sample C, so the MR is decreased by postannealing at 1100 ℃. Therefore, further enhancement of the tunneling magnetoresistance(TMR) can be realized by regulating the grain size at appropriate annealing temperature.