Dynamic Positioning (DP) is used to automatically maintain the position and heading of a floating structure subjected to environmental disturbances. A DP control system is composed of a motion controller to compute the desired force and moment and a thrust allocator to distribute the computed force and moment to multiple thrusters considering mechanical and operational constraints. Among various thruster configurations, azimuth thrusters or propeller/rudder pairs tend to make the allocation problem difficult to solve, because these types of propulsion systems include nonlinear constraints. In this paper, a dynamic positioning strategy for a twin-thruster ship that is propelled by two azimuthing thrusters is addressed, and a thrust allocation method which does not require a numerical optimization solver is proposed. The applicability of the proposed method is demonstrated with an experiment using an autonomous boat.