A three-dimensional time domain approach is used to study nonlinear wave diffraction by a fixed, vertical circular-cylinder that extends to the sea floor. In this approach, the development of the flow can be obtained by a time-stepping procedure, in which the velocity potential of the flow at any instant of time is obtained by the boundary-element method. In the numerical calculations, the exact body-boundary condition is satisfied on the instantaneous wetted surface of the cylinder, and an extended Sommerfeld condition is developed and used as the numerical radiation condition. The fourth-order Adams-Bashford method is employed in the time stepping scheme. Calculations are done to obtain the nonlinear diffraction of solitary waves and Stokes second-order waves by a vertical circular-cylinder. Numerical results are compared with the available linear and second-order wave-force predictions for some given wave height and wavelength conditions, and also with experimental data. Present horizontal force results agree better with the experimental data than the previous predictions.