Bilge keels are effective passive devices in mitigating the rolling motion, and the usage of them covers almost all the sea going vessels. This paper focuses on the viscous effect of the bilge keel, ignored the effect of the free surface and the effect of the ship hull, for the general viscous characteristic of the bilge keel. In order to investigate the viscous effect of the bilge keel on the total damping moment, a special 2 dimensional numerical model, which includes a submerged cylinder with and without bilge keels, is designed for the simulation of forced rolling. Three important factors such as bilge keels width, rolling periods, as well as maximal rolling angles are taken into account, and the viscous flow field around the cylinder is simulated by some codes based on the viscous method in different conditions, in which the three factors are coupled. Verification and validation based on the ITTC method are performed for the cylinder without bilge keels in the conditions of different rolling periods and maximal rolling angles. The primary calculation of damping moment induced by the cylinder with 0mm, 4mm, and 10mm width bilge keels shows some interesting results, and a systematic analysis is conducted. The analysis of the damping moment components suggests there is phase difference between the damping moment induced by the cylinder and the bilge keels, and when the bilge keels width reaches a special size, the total damping moment is mitigated. The calculation of the damping moments induced by the cylinder with some larger bilge keels are also performed, and the results suggest that, the damping moment induced by the bilge keels is increased rapidly and becomes the dominant part in the total damping moment while the width of the bilge keels are increased, but the damping moment induced by the cylinder is not changed significantly. Some illustration of the vortices formation and shedding is included, which is the mechanism of the damping moment caused by the bilge keels. The present work shows an interesting problem, and it is useful for the bilge keel design.