The condition of rolls has a significant influence on the process conditions such as longitudinal tension and lateral error in web transport systems such as metal, film process. Especially a roll shape defect such as an eccentricity is a major cause for the periodic tension disturbance in the web. In this study it is aimed to reject these disturbances caused by unknown shape of rolls. In order to reject the tension disturbance due to the roll shape, an adaptive eccentricity estimator and eccentricity compensation method were proposed. The compensation method including the adaptive eccentricity estimator was tested through the computer simulation and experimental study for its validity.