In view of engine engineering, combustion instability are widely presented in many engines, such as liquid rocket engine, ramjet engine, scramjet engine and SI(spark-ignition) engine, which is harmful to normal operation of engines and even damage the engine in an instant. In this paper, three dimensional numerical simulation of methane premixed gas combustion in a backward-facing step is investigated in an atmosphere pressure. The large eddy simulation and a mixing method of the eddy-dissipation/Arrhenius are used for turbulent combustion model, The two-step methane global reaction is employed for reaction. The effects of different methane premixed gas inlet velocities on backward-facing step combustion stability are studied. When the premixed gas inlet velocity is in high value, the premixed flow can’t be ignited quickly. There is large vorticity near the step and vortex will take the unburned premixed gas to the high-temperature reaction zone. The fuel is rapidly consumed, resulting in a great amount of heat release and the rapidly rising of pressure. This process occurs periodically, causing the oscillation of heat and pressure and ultimately leading to the combustion instability. When the premixed gas inlet velocity decreases, the vorticity near the step is smaller. The premixed gas can be stable ignited and reacts continually. Meanwhile the combustion chamber pressure oscillation is small. While too small inlet velocity will significantly reduce the reaction rate and thus extend the reaction distance.