The electronic structure and magnetic properties of the quasi-1D transition-metal borates PbMBO4 (M = Ti, V, Cr, Mn, Fe, Co) have been investigated by density functional theory, including electronic correlation. The results evidence PbCrBO4 and PbFeBO4 as antiferromagnetic (AFM) semiconductors (intra-chain AFM and inter-chain FM) and PbMnBO4 as a ferromagnetic (FM) semiconductor (both intra- and inter-chain FM) in accordance with experimental observations. For non-synthesized PbTiBO4, PbVBO4, and PbCoBO4, the ground-state magnetic structures are paramagnetic, FM, and paramagnetic, respectively. In this series of compounds, there are two kinds of superexchange couplings dominating their magnetic properties, i.e. the direction M-M delocalization superexchange and indirect M-O-M correlation superexchange. For PbMBO4 with M (3+) d (n) , n ⩽ 3 (M = V and Cr), the main intra-chain spin coupling is the M-M t 2g-t 2g direct delocalization superexchange, while for PbMBO4 with M (3+) d (n) , n > 3 (M = Mn and Fe), the main intra-chain spin coupling is the near 90° M-O-M e g-p-e g indirect correlation superexchange.