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We report that the Fe-rich single-phase Sr2Fe1+xMo1-xO6 (x = 1/9, 1/6 and 1/3) ceramics can be synthesized in a N2 stream by the solid-state reaction method, while the usual Sr2FeMo2O6 (i.e. x = 0) can only be synthesized in a H2+Ar stream. X-ray diffraction shows that all ceramics are well crystallized with tetragonal symmetry. X-ray photoelectron spectroscopy results confirm that the chemical states of interior Fe and Mo cations are significantly more complex than those of the surface cations. With the increase in x, the materials change from ferrimagnetic (x = 0, 1/9, 1/6) to spin-glass-like behaviour (x = 1/3) and the magnetism decreases dramatically. The Curie temperature (Tc) and the magnetoresistance (MR) at 10K with a field of 2 T (Tc, MR) are (400 K, -20.9%), (390 K, -10.3%) and (385 K, -4.5%) for x = 0, 1/9 and x = 1/6, respectively. The results are further analysed by Monte Carlo simulations. Our results show that high-Tc ferrimagnetic double perovskites with good magnetic and transport properties can be obtained conveniently in a N2 stream instead of conventional H2 + Ar, which not only provides a safe and low-cost way to synthesize these materials, but may also be helpful in decreasing the oxygen vacancy concentration. [ABSTRACT FROM AUTHOR]