The problem of a hydromagnetic convective flow of an electrically incompressible viscous conducting fluid past a uniformly moving vertical porous plate is investigated analytically, taking into consideration radiation and thermal diffusion effects. A constant suction velocity is applied to the plate. A uniformly strong magnetic field is supposed to be applied normally to the plate and directed into the fluid region. To find a solution to the problem, an asymptotic series expansion method is used. The effects of thermal diffusion, magnetic field, porosity parameter, thermal radiation, and Grashof number are mainly focused on the discussion of the current problem. Increasing Soret number (Sr) hikes the velocity profile and skin friction but declines Sherwood number. Also, it has been found that, when the magnetic parameter (M) increased, the fluid velocity and the concentration profile decreased.The current results show a good deal of agreement with previously published work. The findings of this study could be relevant in a variety of applications, including diffusion processes involving molecular diffusion of species with molar concentration.