First-principles calculations have been performed to study the modulation of the electronic and optical properties of the black phosphorous carbide monolayer (b-PC) by the adsorption of O-2, H2O, NO2, and NH3 molecules. All the molecules are weakly physisorbed on the surface of the b-PC, which act as electron acceptors except NH3. Especially, O-2 and NO2 molecules can introduce deep acceptor states in the bandgap of the b-PC. The effects of the external electric field and the in-plane strain were further studied. For the b-PC with the adsorbed O-2, the typical p-type doping can be achieved under an appropriate external electric field. However, the b-PC with the adsorbed NO2 is the most susceptible to the in-plane strain, as evidenced by the significant changes in the adsorption energy and the charge transfer under the compressive strain. In addition, the optical absorption of the b-PC can be significantly enhanced upon the adsorption of O-2 and NO2 molecules, which can be further modulated by the external electric field and the in-plane strain. Our calculations predict an effective method to modulate the electronic and optical properties of the b-PC, which may widen its applications in the future electronics and optoelectronics. (C) 2018 Elsevier B.V. All rights reserved.