A numerical method for the two dimensional full nonlinear Radiation-Diffraction problem is developed to simulate the motions of arbitrary shaped 2-D floating body in waves. The mixed Eulerian-Lagrangian method is utilized for the free surface. To calculate the accurate hydrodynamic pressure on the body surface, that is to calculate the accurate acceleration of body, both the velocity field and the acceleration field combined with the equations of body motions are solved. This method enables us to keep the dynamic equilibrium of forces between fluid and floating body on every time step. The Boundary Element Method (BEM) is used to solve the field equations. For illustration, two computational examples are presented in comparison with the experimental data : (i) a transient motion of midship section body in an incident wave ; (ii) a growth of parametric oscillation of roll motion of flare shaped body in a regular wave. These examples show that the computational results are in excellent agreement with measured body motions.