The Taguchi′s orthogonal array method with four factors and four levels is used to carry out the experimental investigation of the Nd∶YAG pulsed laser trepanning drilling of the superalloys with the thickness of 3 mm. The influences of pulse energy, defocusing amount, number of trepanning and trepanning speed on hole taper and hole circularity are analyzed. The laser processing parameters are also optimized and the minimum microhole taper and the relatively better microhole circularity are obtained. The results show that the influences of pulse energy, defocusing amount, number of trepanning, and trepanning speed on microhole circularity are not significant during the laser trepanning drilling process, while the influence of defocusing amount on microhole taper is the most. Moreover, the minimum microhole taper is obtained when using the optimal laser processing parameters as the number of trepanning of 6, trepanning speed of 6 mm/min, pulse energy of 1.5 J, and defocusing amount of -0.5 mm. In addition, the hole circularity at exit is better than that at entry.