Improving power output and reducing costs are crucial to the sustainable development of offshore wind power. In the present study, a dual-rotor wind turbine (DRWT) is proposed to improve wind energy capture efficiency by adding an auxiliary rotor behind the main rotor. The two rotors can be the same size or different sizes. This will result in different aerodynamic characteristics for DRWTs. In this paper, the NREL Offshore Baseline-5 MW and the NREL 750 kW single-rotor wind turbines (SRWTs) are used to configure three different types of DRWTs. The power output and wake characteristics of three different DRWTs with co-rotating (CO-DRWT) and counter-rotating (CR-DRWT) configurations on an actual scale are compared. The Reynolds-averaged Navier–Stokes (RANS) model with k-ω SST (shear stress transport model) is used to simulate the unsteady flow generated by the DRWT’s rotation. The present numerical results show that the power coefficient of the 5 MW-5 MW CO-DRWT can reach 1.22 times that of the 5 MW SRWT. Moreover, a faster wake velocity deficit recovery is found in the 5 MW-5 MW DRWTs because the high-velocity flow caused by the merging and mixing of the trailing vortices of the 5 MW-5 MW DRWTs brings an energy supplement to the wake velocity deficit.