A 2D nonlinear numerical wave tank is developed to simulate the motion responses of a moored floating body in waves which may experience strongly nonlinear wave-body interactions. The numerical solver is based on a Boundary Element Method which has been developed to solve strongly nonlinear hydrodynamic problems. The method is further developed in this paper to simulate a floating body in waves, where horizontal, vertical and rotational motions can be calculated. An effective algorithm is implemented to separate the added mass forces from the total hydrodynamic forces, thus to make the time domain solution converge more easily. The numerical results for a horizontal circular cylinder in waves are compared with linear theory for small wave steepness for verification and further compared with published model tests and CFD results for high wave steepness as validations.