Products coated with flexible film can be stored in wound rolls after the winding process. However, if the roll product experiences excessive internal stress, it can lead to various defects in the coated layer. To alleviate the stress within the wound roll, a taper tension profile is utilized to progressively reduce tension as the winding length increases. As a substantial amount of web is wound onto the core, the moment of inertia of the wound roll increases. It has been observed that, as the winding length increases, the tension control performance of the taper tension tends to deteriorate. We propose an advanced taper tension profile to enhance tension control performance and validates the effectiveness of this profile through winding experiments. It was observed that, compared to the parabolic taper tension, maximum tension error could be reduced by approximately 16.1 % throughout the winding process. This reduction in tension error enables the preservation of the radial stress reduction effect of the taper tension, resulting in a 13.3 % decrease in the maximum radial stress compared to the parabolic taper tension. The proposed taper tension profile contributes to a more uniform quality of the coated layer, especially as the maximum winding length is extended.