• Conjugate heat transfer analysis is performed on an internally and film cooled vane. • A parameterized optimization procedure is developed for film cooling arrays. • All of the film cooling arrays are considered in a multi-objective optimization. • Effects of injection angles and compound angles on film cooling are discussed. To enhance film cooling effectiveness, an optimization of film cooling arrays on a gas turbine vane is carried out by using an integrated approach of numerical simulation and parameterized design. Conjugate heat transfer (CHT) numerical simulation is performed on an internally and film-cooled vane, and the simulation accuracy is validated against the experimental data. The parameterized optimization procedure, which combines CFD simulation with the design of experiment (DOE), back propagation neural network (BPNN), and genetic algorithm (GA), is developed based on the fluid domain of the vane. In the workflow, the data are parameterized and passed across the design, simulation, and optimization. The injection angles and compound angles are optimized. For the adiabatic geometry model used in the optimization process, the downstream average adiabatic film cooling effectiveness achieves a 7.7% increment over the reference design, while the average temperature of the leading edge is decreased by 10.8 K. The obtained optimized design is applied to the CHT computational domain of the vane for further analysis of film cooling characteristics. The area-averaged temperature of the vane surface and the volume-averaged temperature of the solid region are reduced by 7.1 K and 5.8 K, respectively.