In the present study, a numerical analysis is made for unsteady magnetohydrodynamic (MHD) natural convective boundary-layer flow past an impulsively started semi-infinite vertical plate with variable surface temperature and mass flux in the presence of thermal radiation and chemical reaction. The Crank-Nicolson implicit finite difference technique is implemented to solve the system of governing equations. Numerical results are obtained for different values of system parameters and analyzed through graphs. The velocity profiles of the present study have been compared with the available results for the limiting case and a good agreement is found between the results. © 2016 Author(s).