Abstract A Time-domain Higher-Order Boundary Element Method (THOBEM) is developed for simulating wave-current interactions with 3-D floating bodies. Through a Taylor series expansion and a perturbation procedure, the model is formulated to the first-order in the wave steepness and in the current velocity, respectively. The boundary value problem is decomposed into a steady double-body flow problem and an unsteady wave problem. Higher-order boundary integral equation methods are then used to solve the proposed problems with a fourth-order Runge-Kutta method for the time marching. An artificial damping layer is adopted to dissipate the scattering waves. Different from the other time-domain numerical models, which are often focused on the wave-current interaction with restrained bodies, the present model deals with a floating hemisphere. The numerical results of wave forces, wave run-up and body response are all in a close agreement with those obtained by frequency-domain methods. The proposed numerical model is further applied to investigate wave-current interactions with a floating body of complicated geometry. In this work, the regular and focused wave combined with current interacting with a truss-spar platform is investigated.