This paper presents an analytical solution of unsteady one-dimensional natural convective flow of a viscous incompressible and electrically conducting fluid past an infinite vertical cylinder with constant temperature and magnetic field, applied normal to the direction of flow. Exact solutions of dimensionless unsteady linear governing equations are obtained by using Laplace transform technique. Numerical computations for the transient velocity, temperature, skin-friction, Nusselt number are computed and presented in graphs for various set of physical parametric values viz; Grashof number, Prandtl number, magnetic parameter and time.