The weak-stiffness ball-end-milling-cutter is widely used in the milling of deep cavity die parts. The chatter is easy to occur in the machining process. How to determine machining stability region is an important way to enable stable milling. However, the milling system has a characteristic of variable time delay. It is difficult to analyze the milling stability, which restricts the improvement of machining quality. Therefore, a milling stability analysis method for the ball-end-milling-cutter with weak stiffness is proposed. Firstly, the dynamic equation of the cutter system with weak stiffness is established. Then, the time delay of the selected point of the cutter tooth is solved by using Newton-Raphson. Finally, based on the full-discretization method, a stability analysis method considering the regeneration effect with variable delay is proposed, and the critical cutting depth corresponding to different rotational speeds is obtained by the Floquet theorem. The milling stability lobe diagram is constructed. Experimental results show that there are chatter frequencies in the milling force when milling in the unstable region of the lobe diagram. Compared with those of the milled surface in the stable region, the Sy and Sa of the milled surface are increased by 35% and 42% . Results show that the analytical method is reliable, which can provide a basis for the selection and optimization of the cutting parameters.