In this paper, an axisymmetric flow and heat transfer of electrically conducting fluid over a nonlinearly shrinking surface in the presence of magnetic field and suction at the surface is investigated numerically. The shrinking velocity as well as suction at the sheet are assumed to follow the power law of radial distance. A magnetic field is applied normal to the sheet. The governing boundary layer PDEs in cylindrical polar coordinates are reduced into highly nonlinear ordinary differential equations by a similarity transformation. The reduced ODEs are then solved numerically by finite element method for power-law temperature boundary conditions. It is found that radial velocity is decreased with the increase in magnetic field strength and suction at the surface. It is also observed that the thermal boundary layer thickness decreases with the increase in magnetic field strength, suction parameter, power-law index for shrinking velocity and Prandtl number. On the other hand, the thermal boundary layer thickness is increased for increasing values of power-law index for temperature.