In the present study, a three-dimensional computer code, based on the computer software KIVA-3, was developed for the combustion-flow simulation of a bipropellant liquid rocket thruster. A jets-impingement model is proposed for the unlike-doublet jet impingement issue. The computer code is employed to simulate a small bipropellant liquid rocket engine installed with three unlike-doublet injectors of NTO and MMH as well as six fuel injectors injecting MMH toward the combustor wall for cooling. Effects of the fuel-injection cooling on the combustion flow, combustion efficiency, and wall temperature were investigated. The results obtained from the present study show that under the present injector configuration and a constant total fuel-flow rate, higher cooling-fuel ratios make the atomized mixing flow of NTO and MMH shift toward the combustor wall, resulting in lower combustion efficiency and chamber pressure; however, low cooling-fuel ratios are unable to keep the wall-temperature sufficiently low. To overcome this issue, the proposed three-dimensional computer code calculates/locates the optimal cooling-fuel ratio that bears high combustion efficiency for a bipropellant liquid rocket combustor while keeping the chamber wall sufficiently cool.