Two-dimensional conductive metal-organic frameworks (2D c-MOFs), which feature high electrical conductivity and large charge carrier mobility, hold great promise in electronics and optoelectronics. Nevertheless, the limited solubility of commonly used planar ligands inevitably brings challenges in synthesis and purification and causes laborious coordination conditions for screening. Moreover, most reported 2D c-MOFs are polycrystalline powders with relatively low crystallinity and irregular morphology, hindering the unveiling of the detailed structure-function relationship. Herein, we developed a "rotor-stator" molecular design strategy to construct 2D c-MOFs using a delicately designed nonplanar biscarbazole ligand (8OH-DCB). Benefiting from the special "rotor-stator" structure of the ligand, crystals of Cu-DCB-MOF were successfully prepared, allowing for the precise determination of their crystal structure. Interestingly, the crystals of Cu-DCB-MOF can be obtained in various organic solvents, indicating excellent solvent compatibility. The versatility of the "rotor-stator" molecular design strategy was further demonstrated by another two new ligands with a "rotor-stator" structure, and afford corresponding 2D c-MOF crystals (Cu-DCBT-MOF and Cu-DCBBT-MOF). The current work presents a facile approach toward the rational design and direct construction of highly crystalline 2D c-MOFs using nonplanar ligands.