It was mainly aimed at the study to make the optimization of laser parameters to obtain dimples with the desired shape and size. Carbon Fiber EPOXY composite (CF-EPOXY) surfaces were ablated by Nd:YAG laser which has a 1064 nm wavelength. Some important laser process parameters such as focus position, pulse energy, duration and number were optimized to achieve maximum aspect ratio, circular shape and minimum thermal defect. In addition, it has been determined that which laser parameters are more effective to obtain the desired quality surface. These different shapes and geometry of dimples could be used to improve some properties such as wettability, friction, etc. The pulse energy with an effective rate of 55.97 % is the most effective parameter to achieve the larger aspect ratio. The focus position is the most effective parameter with the rates of 66.18 % and 47.94 % to obtain both perfect circularity and minimum thermal defects respectively. Confirmation experiments were performed and the highest aspect ratio was found as 1.14, the best circular dimple and the minimum thermal effects outside the spot area were found with the rates of 1.021. These are the optimum results of 9 experiment sets in this study for each output. The results were supported by confirmation experiments and regression analysis. It can be concluded that the Taguchi method is reliable and saves time and materials.