One of the typical local structures of the freeform surfaces is the concave umbilical structure. This structure is often used in the design of flashlight reflectors, parabolic mirrors, lampshades, car and motorbike headlights, etc. This paper presents research on surface generation accuracy and machining time when 3-axis CNC milling of surfaces with concave umbilical structure. The experimental model has a concave umbilical structure surface designed based on the scanning of the inner surface of the flashlight reflector. The experiment was conducted according to an orthogonal matrix design Taguchi OA9(33). Analysis of variance (ANOVA) of the experimental results show that when finishing milling a surface with a concave umbilical structure, the type of tool path and feed per tooth have a great influence on the machined surface accuracy, while the influence of the cutting speed is quite small. Meanwhile, the effects of cutting speed, feed per tooth and toolpath type on machining time are quite similar. Gray relational analysis (GRA) combined with Taguchi technique is applied for multi-object optimization to achieve high accuracy of the machined surface and the short machining time at the same time.