This paper is concerned with a computational study on the hydroelastic response of a long, straight and side-anchored fjord-crossing floating bridge accounting for the wave-current interaction. The effect of this interaction on a single bridge pontoon is investigated by using the three-dimensional potential solver VERES3D. The frequency-dependent hydrodynamic coefficients and excitation force transfer functions are presented and compared with WAMIT results where the current effect is ignored. Based on the frequency domain results, an approach to account for the wave-current interaction in time domain analysis is proposed. Next, a generic straight and side-anchored floating bridge model is put forward to examine the stochastic structural responses in the time domain. For the purpose of comparison, the bridge responses under waves and current without interaction are also investigated. This study attempts to quantify the wave-current interaction effect on the structural responses of a floating bridge and provide useful recommendations and suggestions to researchers and engineers for their study of similar structures.