Numerical solutions of magnetodynamics (MHD) effects on the free convective flow of an incompressible viscous fluid past a moving semi-infinite vertical cylinder with temperature oscillation are presented. The dimensionless, unsteady, non-linear, and coupled governing partial differential equations are solved by using an implicit finite difference method of the Crank-Nicolson type. The velocity, temperature, and concentration profiles are studied for various parameters. The local skin-friction, the average skinfriction, the Nusselt number, and the Sherwood number are also analyzed and presented graphically. The results are compared with available results in literature, and are found to be in good agreement.