The accurate description of the aerodynamic forces due to free-stream turbulence acting on a stationary bridge deck represents a challenging task. This paper presents a Computational Fluid Dynamics (CFD) approach based on the two-dimensional (2D) Vortex Particle Method (VPM) for simulation of a six-component complex aerodynamic admittance. Deterministic free-stream turbulence is simulated by modeling the wakes of two fictitious pitching airfoils with vortex particles. For out-of- or in-phase sinusoidal oscillations of the airfoils, a longitudinal or vertical sinusoidal gust is obtained along the centerline, respectively. A closed-form relation, based on an existing mathematical model, is deduced to relate the gust amplitudes and vortex particles’ circulation. Positioning a section downstream of the particle release locations yields sinusoidal buffeting forces. The complex aerodynamic admittance is then determined as a transfer function between the buffeting forces and the deterministic freestream turbulence. A verification of the method is performed for the complex Sears’ admittance of a flat plate. Finally, the CFD method is validated against wind tunnel tests for a streamlined bridge deck. The results from both, verification and validation, yielded a good agreement. Applications of the presented method are foreseen in the scope of buffeting analyses of line-like structures under the strip assumption.