The diffraction of nonlinear water waves around a fixed large surface-piercing body of arbitrary shape is solved in three-dimension numerically using second order perturbation theory. A time domain panel method is applied using uniform distribution of sources and doublets on each panel. Based on the above method, a computer program was developed in MATLAB environment and FORTRAN language. A simple radiation boundary condition was proposed by considering constant celerity for the scattered first and second order waves. Numerical results are presented for surface-piercing vertical circular cylinder on a flat bed with initial conditions corresponding to a Stokes second order wave field in the domain. Applying proposed radiation condition made the algorithm simpler and faster, so it reduced the memory storage and CPU time by factors of 1.5 and 1.1, respectively. Employing an efficient cylindrical panelization also reduced the number of panels by a factor of 4.8 relative to ordinary rectangular type panelization. The above modifications have reduced the computer memory storage and CPU time by factors of 14.5 and 7.4, respectively.