Because of the lack of strong pi-interaction in their bonds connecting building units, most of the metal organic frameworks (MOFs) and covalent-organic frameworks (COFs) achieved so far are insulators or wide-bandgap semiconductors. The design of metal-like frameworks based on known chemical components is a challenge. This work reports that aryl borons can be linked together through isocyanides to form stable and easily accessible low-dimensional boronic-organic frameworks (BOFs). Particularly, the boron atoms in the BOFs behave like transition metals, forming the combined a sigma-donation and pi-backdonation bonds instead of the usual electron-sharing bonds with the isocyanide linkers. This peculiar bonding endows BOFs with semimetal and narrow-bandgap semiconductor features, which are different from MOFs and COFs and may be found to be useful in future nanoelectronics. The results open a door to integrating the knowledge of the donor-acceptor chemistry in the main group into materials science.