The problem of second-order wave diffraction around arbitrary two-dimensional bodies is studied and a numerical method in time-domain presented. The solution is based on separating the velocity potential into a known incident velocity potential and a scattered velocity potential. The initial condition corresponds to Stokes second order wave field in the domain, and the scattered potential is allowed to develop in time and space. The free surface boundary conditions and the radiation condition are satisfied to second order by an integral equation in time and the field solution at each time step is obtained by an integral equation method based on Green's theorem. Results are presented for three different geometries, a semi-submerged cylinder with axis at the still water level, a fully submerged circular cylinder and a semi-submerged rectangular cylinder. Comparison of the results of this work with theoretical and experimental ones shows good agreement.