The extremely large magnetoresistance (XMR) observed in many topologically nontrivial and trivial semimetals has attracted much attention in relation to its underlying physical mechanism. In this paper, by combining the band structure and Fermi surface (FS) calculations with the Hall resistivity and de Haas-van Alphen (dHvA) oscillation measurements, we studied the anisotropy of magnetoresistance (MR) of ReO3 with a simple cubic structure, an "ordinary" nonmagnetic metal considered previously. We found that ReO3 exhibits almost all the characteristics of XMR semimetals: the nearly quadratic field dependence of MR, a field-induced upturn in resistivity followed by a plateau at low temperatures, and high mobilities of charge carriers. It was found that for magnetic field H applied along the c axis, the MR exhibits an unsaturated H-1.75 dependence, which was argued to arise from the complete carrier compensation supported by the Hall resistivity measurements. For H applied along the direction of 15 degrees relative to the c axis, an unsaturated H-1.90 dependence of MR up to (9.43 x 10(3))% at 10 K and 9 T was observed, which was explained by the existence of electron open orbits extending along the k(x) direction. Two mechanisms responsible for XMR observed usually in the semimetals occur also in the simple metal ReO3 due to its peculiar FS (two closed electron pockets and one open electron pocket), once again indicating that the details of FS geometrical configuration are a key factor for the observed XMR in materials.