The structural and electronic properties of pure graphene, graphene with a vacancy, graphene with two vacancies and molybdenum-doped graphene were investigated. In addition, the adsorption of Mo atoms on graphene (G), reduced graphene (rG) and reduced graphene oxide (rGO) was examined. The possible energies of different active adsorption sites of nanostructured Mo-decorated G, rG and rGO have been calculated using density functional theory (DFT). Mo atoms are predicted to create bonds with six C atoms in G, three C atoms in rG, and both C and O atoms in rGO sheets after geometry optimizations. The study focused on changing the electronic structure of G, including opening the zero band gap and controlling the band structure, which was done by creating defects and adding impurities. The present study revealed a significant correlation between the adsorption of the Mo atom and the characteristics exhibited by frontier orbitals. The results indicated that the adsorption characteristics of Mo atoms in pure G, rG and rGO are different, despite chemisorption being the common mechanism. Specifically, Mo-decorated rG exhibited higher adsorption energy, while Mo-decorated G demonstrated a lower adsorption energy. According to these findings, it is reasonable to anticipate that Mo-decorated rG could be applied as a novel adsorbent for the removal of pollutants.