Two-dimensional conjugated metal-organic frameworks (2D c-MOFs) are emerging as a unique class of electronic materials. However, 2D c-MOFs with band gaps in the Vis-NIR and high charge carrier mobility are rare. Most of the reported semiconducting 2D c-MOFs are metallic (i.e. gapless), which largely limits their use in logic devices. Herein, we design a phenanthrotriphenylene-based, D2h-symmetric π-extended ligand (OHPTP), and synthesize the first rhombic 2D c-MOF single crystals (Cu2(OHPTP)). The continuous rotation electron diffraction (cRED) analysis unveils the orthorhombic crystal structure at the atomic level with a unique AB layer stacking. The Cu2(OHPTP) is a p-type semiconductor with an indirect band gap of ~0.50 eV and exhibits high electrical conductivity of 0.10 S cm-1 and high charge carrier mobility of ~10.0 cm 2 V-1 s-1. Theoretical calculations underline the predominant role of the out-of-plane charge transport in this semiquinone-based 2D c-MOF.