In the chemical laser system with a radial expansion nozzle array, the laser beam generation is achieved by mixing F atom from supersonic nozzle and $D_{2}$ molecule from holes of round-bended supply line. Based on that the fuel injection angle with main stream has a great influence of performance on supersonic combustor, the effects of $D_{2}$ injection angles with the main F flow on mixing enhancement are numerically investigated. The results are discussed by comparison with three cases of $D_{2}$ injection angles; $10^{o}$, $20^{o}$ and $40^{o}$ with the main flow direction. Major results reveal that as the $D_{2}$ injection angle increases, the maximum small signal gains and the static pressure in the laser cavity become higher. Consequently, the $D_{2}$ injection angle between $20^{o}$ and $40^{o}$ is recommended as an optimized geometric parameter in consideration of both of high gains and low cavity pressure.