Zirconia Toughened Alumina (ZTA) ceramic composite offers excellent mechanical properties. Therefore, medical implant, cutting tools, and structural parts are fabricated by the ZTA. Many applications of ZTA requires circular hole in it. Conventional circular hole making methods are not preferred due to hostile machining characteristics of ZTA. However, laser circular cutting or laser trepan drilling (LTD) is a better option among available non-conventional hole making methods. But optimum selection of laser trepanning parameters value for ZTA to get quality hole circularity with minimum taper is challenging. In the present research paper, optimum set of input parameters to optimize the multi-objective responses of the drilled hole is investigated. A multi-objective response of the drilled hole is considered as top and bottom circularity and taper during laser trepan drilling in ZTA plate. The mathematical equation of the multi-objective functions are developed using artificial neural network. The research findings show an overall improvement of approximately 12% in multiple quality characteristics. Further, optimum results have been verified with confirmation experiment that shows small variation of 3.9%.