A numerical analysis was performed on the fluid flow in injector orifice of a liquid rocket engine. The present computational code was verified against the published data for turbulent flow in a pipe with a sudden expansion-contraction. Considered were the parameters for the flow analysis in an injector orifice: Reynolds number, ratio of mass flow rate of the injector orifice and inlet flow rate, and slant angle of the injector orifice. The discharge coefficient increased slightly as the Reynolds number increased. The slant angle of the injector changed critically the discharge coefficient. The discharge coefficient increased by 7% when the slant angle changed from $-30^{circ}$ to $30^{circ}$ The ratio of mass flow rate had relatively little impact on the discharge coefficient.