A fast and furnace-free method of combustion synthesis is employed for the first time to synthesize iron-based superconductors. Using this method, Fe1.1Se1-xTex (0≤x≤1) samples can be prepared from self-sustained reactions of element powders in only tens of seconds. The obtained Fe1.1Se1-xTex samples show clear zero resistivity and corresponding magnetic susceptibility drop at around 10-14 K. The Fe1.1Se0.33Te0.67 sample shows the highest onset Tc of about 14 K, and its upper critical field is estimated to be approximately 54 T. Compared with conventional solid state reaction for preparing polycrystalline FeSe samples, combustion synthesis exhibits much-reduced time and energy consumption, but offers comparable superconducting properties. It is expected that the combustion synthesis method is available for preparing plenty of iron-based superconductors, and in this direction further related work is in progress.