A fixing device for an automobile muffler is constructed to effectively support and minimize the vertical and transverse movement of a muffler in relation to a car body via a resilient hanger that is diagonally angled. The rear part of the resilient hanger is attached with a cover bracket and a body side bracket, wherein the cover bracket is formed with a vertical flange surface and the body side bracket is formed with a vertical protrusion surface, thereby effectively support any longitudinal movement of the muffler against the vehicle, and increasing the rigidity of connecting parts between the muffler and an exhaust pipe via the cover bracket.