In this study we investigated the effects of free convection flow of a viscoelastic second-grade fluid along a vertical flat surface with power-law temperature distribution. The boundary layer equations for the momentum and the energy transport have been reduced to local similarity equations using appropriate transformations. Solutions of the reduced equations are obtained employing the local non-similarity method as well as the implicit finite difference method against xi ( the local Deborah number) in the range [ 0, 10] for fluids having Prandtl numbers of 10, 50, and 100. The regular perturbation solutions are also been obtained for smaller values of xi together with the Pade approximation. Results thus obtained are discussed in terms of the local skin friction and local rate of heat transfer for different values of the physical parameters, like n and Pr. Effect of the Deborah number, De, on the velocity and temperature profiles has also been shown graphically. It is observed that both the local skin friction and heat transfer coefficients decrease with increase in the value of De for given values of n and Pr.