Throughout the history, material removal has been achieved by different types of conventional machining processes such as milling, drilling, and turning operations etc. These machining processes depend on the mechanical and chemical properties, geometry, and cost of material. Drilling operation is one of the most used machining operations due to high demand and applications in many industries such as aerospace, automotive, oil and gas, and biomedical industry. Most of these applications wanting drilling operation to be executed on irregular non-flat surfaces such as convex surfaces. In the aerospace industry, convex spherical surface drilling is used to create holes on aircraft components, such as engine parts, airframe components, and wing surfaces. It is important to understand the drilling process and its affecting parameters to increase the drillability of the manufactured part with convex surfaces. It has been observed that the drilling performance on spherical surface have been rarely studied in the literature. Therefore, in this study, drilling performance of convex surface profiles made out of Ti6Al4V was investigated numerically with the help of Finite Element Modeling. The study was conducted numerically by using the Taguchi design of experimentation, and involved the input parameters namely sphere diameter, feed, point angle and spindle revolution. The output responses were cutting force components, power, torque, cutting temperature and material removal rate. The study also implemented multi-objective optimization using desirability function analysis to optimize the convex surface drilling process. It has been found that sphere diameter of 60mm, feed of 0.6 mm/rev, point angle of 140 degrees and spindle speed of 2000 rpm provided the optimum set of parameters to get desirable cutting performance with lowest power consumption.