Aerodynamics of a floating horizontal-axis wind turbine (FHAWT) is subject to its platform’s six degrees of freedom (DOFs) motion, especially the surge motion, and may become much more complicated than that of a fixed-base wind turbine. This paper aims at investigating the aerodynamics of the FHAWT’s rotor and the characteristics of its wake under surge motion. To explore this, a CFD method with the improved delayed detached eddy simulation (IDDES) is applied to a 1:50 model FHAWT. First, it is demonstrated that the rotor’s aerodynamics including the thrust, torque and rotor power may be greatly affected by surge motion even though it is small. During surge motion, the light dynamic stall and rotor-wake interaction phenomena are observed. In addition, the near and far wake may be obviously influenced by surge motion. More importantly, the wake-recovery process under surge motion is slower than the one without surge motion. In general, the surge motion impacts the aerodynamics of the FHAWTs’ rotor and the characteristics of its wake greatly, therefore should receive due attention in the design procedure and the arrangement of wind farms. •IDDES is employed to analyze the surge effect on aerodynamics of a FHAWT.•Surge effect on the rotor aerodynamics is investigated.•Dynamic light stall phenomenon is identified.•Surge effect on the wake characteristics is observed and explained.•Slow wake-recovery process under surge motion is found.