Invar 36 alloy has an extremely low coefficient of thermal expansion and is suitable for preparing a fine metal mask (FMM) for the evaporation of silicon-based organic light emitting display microdisplays. The higher the resolution and the greater the number of pixels, the finer and more delicate the holes required. Femtosecond laser processing technology is an effective technical means for processing Invar 36 alloy FMM due to its characteristics of extremely short pulse width, extremely high pulse energy density, smaller heat-affected zone, and more regular machining edges. The femtosecond laser processing parameters directly affect temperature distribution and then affect the manufacturing quality and efficiency of Invar 36 alloy FMM. At present, femtosecond laser processing of Invar 36 alloy FMM is still in the exploration stage, and the processing mechanism and technology are not clear. In this paper, a simulation model of single-pulse femtosecond laser processing Invar 36 alloy is established based on the two-temperature equation. By comparing the ablation morphology of the simulation output with the experimental measurement results, the validity of the simulation model is verified and the processing mechanism is preliminarily explored. Based on the simulation model, the effects of femtosecond laser energy density, pulse duration, and spot diameter on the electron temperature field, lattice temperature field, and ablation morphology of the craters are explored. The process window of laser processing parameters is determined. A full-factor test is conducted. Take the minimum length of the heat-affected zone, the maximum depth of the ablation crater, and the minimum diameter of the ablation crater as three optimization objectives and obtain Pareto optimal solutions based on genetic algorithm. The optimization of single-pulse femtosecond laser drilling Invar 36 alloy is realized.