In this paper, a new mathematical model describing manoeuvring motions of a ship is presented according to the detailed investigation of captive model tests. This model, based on the method proposed by the subcommittee of JTTC named Group-MMG, is composed of individual characteristics of hull, propeller and rudder and their interactions. First, the model for longitudinal hydrodynamic forces is dealt with. Second, the method to describe the hydrodynamic forces concerning to rudder is treated. A simple model consisting of open characteristics of rudder, inflow angle and velocity at rudder is proposed. Two problems as to lateral hydrodynamic forces acting on hull are then argued. One of them is the matter of nonlinear terms and, from the practical point of view, third order terms with rate of turn and swaying velocity are recommended. The other factor is the fin effect of propeller, and it is verified not to be negligible for manoeuvrability. Last, comparing the free-running results with estimated manoeuvres calculated by the present model, satisfactory coincidence is obtained. Consequently, the proposed model describing manoeuvring motions of a ship is found promising.