The Markov chain model has been proved viable for the airborne contaminant transport simulation. However, its performance should be further validated and improved when there is a contaminant source in the airflow field. This study proposed a novel method that couples the concentration response factor method into a Markov chain model, termed the CRFMC method, to simulate the release and transport of airborne contaminant. The accuracy of the proposed CRFMC method was validated based on two example flow fields, i.e., a 2D isothermal case and a 3D ventilated chamber case. Different contaminant source types, including point, line, area, and volume source (in 3D case only) with constant, linear, exponential, and periodic release strengths were considered. Furthermore, the influence of the pulse type in the CRFMC method on accuracy was evaluated. Results revealed that the CRFMC method is sufficiently accurate for the airborne contaminant transport simulation with a source release. The L2 relative error between the CRFMC method and scalar transport simulation ranges from 9.4% to 16.1% in 2D cases and from 14.9% to 33.4% in 3D cases. This study can aid the development of a Markov chain model for airborne contaminant transport.