This study examined the simultaneous removal and recovery of volatile organic compounds (VOCs) from nitrogen streams using the vapor permeation (VP) technique. A poly(dimethylsiloxane) (PDMS) membrane was employed to separate toluene, m-xylene, and methanol from nitrogen gas. The effects of operating conditions (including PDMS cross-linker content, membrane thickness, feed flow rate, downstream pressure, and VOC feed concentration) on VOC removal were studied. The sorption isotherms and diffusion coefficients of the vapors in the PDMS were established using the gravimetric method. The Flory-Huggins equation was used to fit the vapor sorption isotherms in PDMS. The diffusivity dependence on vapor concentration were fitted using Long's model. The concentration distribution of the vapor in each layer was determined using a stack of membranes consisting of four layers. The measured permeant concentration distribution agreed excellently with the concentration profile calculation. The solution-diffusion model based on the first Fick's law can describe the mass-transfer mechanism of the vapors in a VP process.