A fully nonlinear interaction between random waves and a freely floating body is investigated by a fully nonlinear numerical wave tank (NWT) based on boundary integral equation method (BIEM). In this model, a linear element method is adopted to solve the boundary integral equation, and subsequently the nonlinear free surface is traced by Mixed Eulerian-Lagrangian method (MEL) with a cubic spline scheme and a 4th order Runge-Kutta method. In addition, a JONSWAP random wave is generated by a feeding function based on the Stokes wave theory and the superposition principle for linear waves, and two damping zones are implemented on both ends of NWT to absorb reflected waves scattered by the floating body and to dissipate the transmitted wave energy passing over the body. The hydrodynamic forces are calculated by an acceleration potential method developed by Tanizawa (1995) and a mode-decomposition method. The results of the test of numerical wave generation show that this model is suitable for long time simulation with the reflection coefficient only about 4% for random waves. For regular wave cases, the simulated results show well agreement with linear solution and other numerical models. Finally, we found that if the results of body motions induced by regular waves are multiplied by 1/4, then their comparisons with that of random waves show a good agreement. Moreover, the results of drift force from both regular and random waves have similar trends except at the resonance region.