The onset of natural convection in a horizontal layer of Oldroyd-B Fluid heated isothermally from below is investigated by using linear stability theory. It is known that convective instabilities in the Oldroyd-B fluid layer set in more easily than those of Newtonian fluid and oscillatory motions caused by overstability will occur at the onset of natural convection. Also, it is shown that the Oldroyd-B fluid layer becomes more stable with a larger Biot number, a smaller stress relaxation time and a larger strian retardation time. The layer of Oldroyd-B fluid becomes more stable with decreasing the Prandtl number and the critical conditions are almost independent of the Prandtl number in the range of the Prandtl number values larger than 100. It is clear that the buoyancy effect and the surface tension effect reinforce each other at the onset of natural convection.