In this research, the water spray injection process in a natural-gas-fueled gas turbine combustor is studied numerically using an Eulerian-Lagrangian formulation, and the combined effect of different design variables, including the swirl number, water injection mass flow rate, injection partitioning between a pre-and a post-flame injector, and injection direction, are investigated on several combustor performance objectives by systematic multi-objective optimizations. Sensitivity analyses reveal that the most effectual parameter changing the combustion efficiency and overall emission is the swirl number while the outlet maximum temperature and liquid water mass loading are most sensitive to the post-flame and pre-flame injection mass flow rates, respectively. In addition, the outlet temperature uniformity depends on all the four design variables nearly the same. As the optimal design criteria, multi-objective optimizations propose a high swirl number, a small injection angle, and introducing 81% of the total water at the post-flame injector. The optimal total water-to-fuel ratio is 3.4. However, if the flame instability due to the pressure pulsation becomes critical, this value should be lowered to 2. The optimal designs can reduce both maximum temperature and temperature non-uniformity by 19% and suppress NOx and overall emission by 87% and 110%, respectively.