Abstract The electronic structure of a single MoS2 monolayer is investigated with all electron first-principles calculations based on Kohn Sham Density Functional Theory and variational treatment of spin–orbital coupling. The topologies of the valence band maximum and conduction band minimum are explored over the whole Brillouin zone. The single MoS2 monolayer is confirmed to be a direct band gap semiconductor. The projected density of states (PDOS) of a single monolayer is calculated and compared to that of bulk MoS2. The effective masses and the orbital character of the band edges at high-symmetry points of the Brillouin zone are determined. The spin-splittings of the conduction band minimum (CBMIN) and valence band maximum (VBMAX) are calculated over the whole Brillouin zone. It is found that the maximum spin-splitting of VBMAX is attained at the K point of the Brillouin zone and is responsible for the experimentally observed splitting between the A1 and B1 excitons.