Transition metal dichalcogenides (TMDs) display unique properties in their monolayer structures, namely a direct band-gap transition, which becomes a promising candidate for optoelectronics applications. Among them, WS2 exhibits strong spin-orbit interaction which splits the excitonic peaks as observed in the experimental data up to ~400 meV. Unlike the other TMDs, the first excitonic peak A is very sharp for WS2, while the secondary peak B is broader with smaller relative intensity. In this paper, we perform first-principles calculations on the electronic band structure and solve the Bethe-Salpeter equation for the complex dielectric function of monolayer WS2 to study the effects of spin-orbit coupling on its excitonic structures. To resolve the excitonic peaks, in particular the B peak, we implement the double-grid method. We discuss the effects of electron-hole interaction on the absorption spectrum by comparing it with that calculated at the independent-particle level.