In this paper, we propose a new application of a recent semi-numerical successive linearization method (SLM) in solving highly coupled, nonlinear boundary value problem. The method is presented in detail by solving the problem of steady flow of mixed convection and an incompressible viscous hydromagnetic fluid from a vertical flat plate embedded in a fluid-saturated porous medium. The governing partial differential equations are transformed into a system of ordinary differential equations and then solved by SLM. The effects of different physical parameters on the velocity, temperature, and concentration profiles are determined and discussed. The skin-friction, and heat and mass transfer coefficients have been obtained and analyzed for various physical parametric values. The results are presented numerically through graphs and tables for both assisting and opposing flows to observe the effects of various parameters encountered in the equations.