This article discusses the stagnation-point flow of second grade fluid over an unsteady stretching surface in the presence of variable free stream. Flow analysis has been carried out with heat transfer analysis. The resulting partial differential equations have been converted into ordinary differential equations by employing the suitable transformations. Computations of dimensionless velocity and temperature fields have been performed by using homotopy analysis method (HAM). Graphs are plotted to examine the behaviors of arising physical parameters on the dimensionless velocity and temperature. Numerical values of skin-friction coefficient and local Nusselt number are computed and examined.