The ignition characteristics in a confined axisymmetric coflow $CH_4$ jet were investigated numerically with the Fire Dynamics Simulator(FDS). The $CH_4$ fuel stream was diluted with main combustion product gases, such as $O_2$, $N_2$, CO, $CO_2$, and $H_2O$, and the mixed fuel stream was heated up to the sufficient temperature where a supplying fuel stream can be ignited. For the calculation of chemical reaction in the simulation, a 2-step global finite chemistry model was considered. Boundary condition for confined wall was optimized by investigating the effects of wall temperature on the ignition characteristics of fuel stream. In addition, the effects of composition of diluents in the fuel stream and fuel stream temperature on the ignition of fuel steam were investigated. The ignition characteristics of $CH_4$ stream with diluents were very sensitive to the wall temperature, composition of diluents in the fuel stream and fuel stream temperature.