A transition metal (TM) doped InN monolayer has demonstrated with superior behavior for gas adsorption and sensing. For this paper, we studied the adsorption behavior of a Pd-doped InN (Pd-InN) monolayer upon CO and NO using the first-principles theory. Our results show that the Pd-InN monolayer has a stronger interaction with the CO molecule, compared with the NO molecule, with larger adsorption energy of 2.12 eV, compared to −1.65 eV. On the other hand, the Pd-InN monolayer undergoes more obvious deformation of the electronic behavior in the NO system, making the surface become semimetallic with a 0 eV band gap. Thus, the Pd-InN monolayer could be a promising candidate as a resistance-type sensor for NO detection and as a gas adsorbent for CO removal. We are hopeful that this work can offer the basic physicochemical properties and potential applications of the Pd-InN monolayer, which is beneficial for its further exploration in many fields.