In this paper we show that Sun-viewing images obtained by the Mars Science Laboratory (MSL) Navigation Cameras (Navcam) can be used for retrieving the dust optical depth and constrain the aerosol physical properties at Gale Crater by evaluating the sky brightness as a function of the scattering angle. We have used 65 Sun-pointing images covering a period of almost three Martian years, from MSL mission sol 21 to sol 1646 (MY 31 to 33). Radiometric calibration and geometric reduction were performed on MSL Navcam raw image data records to provide the observed sky radiance as a function of the scattering angle for the near-Sun region (scattering angle from 4{deg} to 30{deg}). These curves were fitted with a multiple scattering radiative transfer model for a plane-parallel Martian atmosphere model using the discrete ordinates method. Modelled sky brightness curves were generated as a function of two parameters: the aerosol particle size distribution effective radius and the dust column optical depth at the surface. A retrieval scheme was implemented for deriving the parameters that generated the best fitting curve under a least-square error criterion. The obtained results present a good agreement with previous work, showing the seasonal dependence of both dust column optical depth and the effectiveparticle radius.