Dual-rotor wind turbines (DRWTs) have attracted the attention of academia and industry for higher wind energy capture efficiency. However, there is still a lack of a public design scheme for the DRWTs to study. To promote the development of the DRWTs, this paper proposed a conceptual design scheme for reference. First, a preliminary design of DRWT is proposed based on the NREL-5MW baseline wind turbine. Then, strength analysis and strengthening design are conducted for the DRWT tower. Simulation results show that the preliminary designed tower has a maximum stress of 206.43 MPa, close to the maximum allowable stress. The strengthening tower with a bottom diameter of 9 m has a maximum stress of 101.97 MPa and the strengthening tower with a bottom thickness of 0.054 m has a maximum stress of 119.53 MPa. For the consideration of cost, the tower with a bottom thickness of 0.054 m is recommended. The proposed conceptual design scheme of DRWT can have rich data and high reliability, which can provide a reference for related research.