In this work, we have investigated the structural and electronic properties of both bulk and monolayer MoS2 based on the density functional theory (DFT) implemented in the CASTEP of Materials Studio package. The calculations are performed with the local density approximation (LDA) and generalized gradient approximation (GGA) functionals for crystal structure optimization and band structure of MoS2 bulk and monolayer. Our calculations show that the GGA functional calculated excellent band gap for bulk MoS2, while LDA functional is found to perform better for band gap calculations of a monolayer. The influence of composition in the energy bands has been realized by analyzing the partial density of states (PDOS) of each atom and density of states (DOS). By reducing the layer thickness from bulk to monolayer, it is found that band structure has the transitions from indirect band gap in the bulk MoS2 (1.53 eV) to direct band gap in the monolayer (1.82 eV). On the other hand, the charge density difference along z-direction shows that the major charge transfer occurs on the surface of the S atoms and there is a little accumulation around the surface of the Mo atoms. This property highlights the promising of MoS2 in improving the fabrication of optoelectronic devices in the future.