Charge and orbital ordering, magnetic state, and exchange couplings in quasi-one-dimensional vanadate V6O13, a potential cathode material for Li-ion batteries, are investigated using the density functional theory with Coulomb interaction correction method (DFT + U). While the difference between t2g orbital occupancies of V4+ (with a nominal 3d1electronic configuration) and V5+ ions is large and gives direct evidence for charge and orbital ordering, the screening is so effective that the total 3d charge disproportionation is rather small. Our results show that the occupied t2g states of V4+ ions in the single V–V layer form a spin-singlet molecular orbital, while the rest half of V4+ ions in the structurally distinct double V–V layers order antiferromagnetically in the low-temperature insulating phase of V6O13. We conclude that the metal-insulator transition and low-temperature magnetic properties of V6O13 involve the spin-Peierls transition assisted by orbital ordering and concomitant distortions of the crystal structure. © 2022, The Author(s).