In this paper a linear diffraction method is presented which is able to determine accurately and fast the effect of current on motions of, and first- and second-order wave loads on offshore structures. The current flow is modeled by double-body potential flow, thereby neglecting viscous effects and stationary wave effects. The interaction between the double-body flow and the first-order non-stationary flow is modeled up to first order in the current speed, thereby restricting the method to small current speeds. A direct pressure integration method is used to evaluate the wave drift forces. Therefore, the gradient of the double-body velocities is required, which is evaluated using an additional boundary integral. The interaction between the double-body flow and the non-stationary flow leads to a modified free-surface condition which is satisfied using panels on the free surface. On these panels pulsating sources are placed satisfying the zero-speed free surface condition in the frequency domain. The method is validated against results published by Zhao and Faltinsen for a fixed vertical truncated cylinder. Furthermore, experimental data for a tanker, published by Wichers,  is used to validate the method for realistic ship shapes. In both cases a good agreement is obtained.