The previous paper which we reported before described a kind of damping function in the equation of single degree of freedom rolling motion which applicable to small fishing vessels. There is no problem in the application of the damping function to the free roll motion in the absence of the roll excitation moment, however there is something wrong in the case of the roll motion with roll excitation moment. This paper describes improvement on the above problem with consideration for the characteristics of angle-dependent damping. And, this paper describes a new method that is able to estimate the characteristics of roll damping in the case of large roll amplitude from free-decay data in the case of small roll amplitude. This method is based on an approximative solution by the averaging method and an analytical solution of the equation of the rolling motion. This method is useful in that it is not necessary to use many data to estimate.