The aim of this paper is to study numerically, magneto-convective non-Newtonian Tangent Hyperbolic boundary layer flow over a circular cylinder. The non-dimensional governing nonlinear coupled partial differential equations are solved by using finite element method. The computational numerical quantities for different parameters which govern the momentum and thermal boundary layers are described quantitatively and epitomized vividly. The numerical results of the skin friction, Nusselt number within the flow regime are compared to validate with the previously reported results in some limiting cases of the present analysis, and are found to be in good agreement.