The newly-discovered B40 is the first experimentally observed all-boron fullerene and has potential applications in molecular devices. Herein, we report the electronic transport properties of B40 and its metallofullerene, Sr@B40, using the first-principles technique. We obtain the conductance of B40 fullerene, which is about 130 μS and can be increased by embedding a strontium metal atom in the cage due to the decreased energy gap. Both the current-voltage (I-V) curves of B40 and Sr@B40 present perfect linear characteristics. Intuitively, it is assumed that the electron currents pass through the B40 fullerene mainly along the surface B-B bonds, while two types of new B-Sr-B bond currents and B→Sr→B hopping currents are presented for Sr@B40 due to Sr acting as a bridge. This study provides valuable information for the potential applications of future borospherene-based molecular devices.