The modification of the electronic structure of bilayer MoS2 by an external electric field can have potential applications in optoelectronics and valleytronics. Nevertheless, the underlying physical mechanism is not clearly understood, especially the effects of the van der Waals interaction. In this study, the spin orbit-coupled electronic structure of bilayer MoS2 has been investigated using the first-principle density functional theory. We find that the van der Waals interaction as well as the interlayer distance has significant effects on the band structure. When the interlayer distance of bilayer MoS2 increases from 0.614 nm to 0.71 nm, the indirect gap between the Γ and Λ points increases from 1.25 eV to 1.70 eV. Meanwhile, the energy gap of bilayer MoS2 transforms from an indirect one to a direct one. An external electric field can shift down (up) the energy bands of the bottom (top) MoS2 layer and also breaks the inversion symmetry of bilayer MoS2. As a result, the electric field can affect the band gaps, the spin-orbit interaction and splits the valance bands into two groups. The present study can help us understand more about the electronic structures of MoS2 materials for potential applications in electronics and optoelectronics.