To harness wind energy resources from the ocean, floating offshore wind turbines (FOWTs) are gaining increasing attention within the industry. In this paper, the impact of platform motion on the aerodynamic characteristics of the FOWT array is numerically investigated. A high-fidelity numerical tool with the Computational Fluid Dynamics (CFD) method is further developed based on the open-source CFD toolbox OpenFOAM by coupling the Actuator Line Model (ALM). The FOWT arrays consisting of three semi-submersible platforms and NREL 5 MW turbines with different arrangements based on tandem and staggered layouts are simulated, and their dynamic response and wake interactions are analysed under regular wave conditions. Results show that in gridded layouts, the downstream turbine experiences the most significant wind velocity reduction due to wake interference, compared with the staggered layouts. In the most common scenarios, the capacity factor of the total system of a tandem layout is 50%, while it is 92% for the staggered layouts. It is also found that whether the third downstream turbine is fixed or not has a minor influence on the time-averaged power output. However, the motion of the turbine, due to the floating platform, significantly influences power fluctuation. In gridded layouts, the downstream FOWT can have up to 25% higher fluctuation amplitude than fixed one, while for staggered layouts, this can reach 80% in the most critical case. It is also observed that strong wind turbulence reduces the impact of platform motion on power fluctuations, especially for the third turbine. By analysing the power output and the platform motion, it is found that the pitch and surge motion of the present OC4 platform have an opposite influence on the power output. Thus, a coupled model considering both degrees of freedom is necessary.