A vector radiative transfer numerical model of the coupled ocean-atmosphere system is developed based on the matrix-operator method,which is named PCOART.Using the Fourier analysis,the vector radiative transfer equation (VRTE) is separated into a set of equations depending only on the observation zenith angle.Using the Gaussian-Quadrature method,VRTE is finally transferred into the matrix equation solved by the adding-doubling method.According to the reflective and refractive properties of the ocean-atmosphere interface,the vector radiative transfer numerical model of the ocean and atmosphere is coupled in PCOART.Compared with the exact Rayleigh scattering look-up tables of MODIS (Moderate-resolution Imaging Spectroradiometer),it is shown that PCOART is an exactly numerical model,and the processing methods of the multi-scattering and polarization are correct.Also,validated with the standard problems of the radiative transfer in water,it is shown that PCOART can be used to calculate the underwater radiative transfer problems.Therefore,PCOART is a useful tool for exactly calculating the vector radiative transfer of the coupled ocean-atmosphere system,which can be used to study the polarization properties of the radiance in the whole ocean-atmosphere system and the remote sensing of the atmosphere and ocean.