The effect of CO and NO adsorption on graphene (pristine, vacancy and doped) were investigated for structural and electronic properties. The sensitivity of palladium (Pd) doped graphene toward small gas molecules CO and NO have been investigated by using DFT calculation within Generalized Gradient Approximation (GGA) as implemented in DMol(3) and CASTEP. The density of states, the most stable adsorption site and adsorption energy of these small gas molecules on vacancy graphene and Pd-doped vacancy graphene are thoroughly discussed. It is found that Pd doping significantly enhances the strength of interaction between adsorbed molecules and the modified substrates. The most stable adsorption site for CO and NO on all graphene sheets are identified and reported. The results present the potential of vacancy graphene and Pd-doped vacancy graphene for molecules sensor application. Novelty: The novelty of this paper is the doping of Pd on vacancy graphene surface could enhance the adsorption energy of CO and NO gas molecules. Besides, most of the studies not using Pd on vacancy graphene to study its effect on small molecules.