The cut geometry prediction, especially the issue regarding computational time, of a complex part surface in five-axis milling remains as a challenge. In this study, the analytical boundary method, which was developed to predict the cut geometry during semifinish milling, was extended by adding a curve boundary algorithm. The extended algorithm made the method applicable not only for workpieces with a straight staircase profile but also for those with a nonstraight one. The proposed method was tested using two parts with different surface shapes. Results demonstrated that the proposed method is applicable for defining instantaneous cut geometry. The verification test proved that the method was accurate when the engagement point was on the top and straight wall surfaces. Relatively small errors were observed when the engagement point was on the nonstraight surface. Moreover, the test on computational time verified the efficiency of the developed method.