Abstarct: Non-newtonian fluids have a huge application in many fields such as military, medical and industrial activities which has attracted great attentions from many years ago. Science of non-newtonian fluids flow is termed Rheology and due to special properties of these kinds of fluids, different behaviors are observed by these fluids. The purpose of this research is to investigation the viscoelastic fluid flow and heat transfer in a curved pipe, analytically. In this research, appropriate approximate solution for viscoelastic fluid flow is suggested using a second order fluid and perturbation solution. The heat transfer analysis of this fluid flow has been achieved. This has been performed using Oldroyd-B model of viscoelastic fluid. The results of second order fluid investigation, indicates that the increment of Weissenberg number enhances the intensity of secondary flows. In addition, this leads to further tendency of Taylor vortices and maximum axial velocity position toward outer wall. Also drag reduction in curved pipe will occur by increasing of retardation time. Heat transfer analysis of Oldroyd-B and SOF flows, indicates the similar results. Increasing of Weissenberg number has a major effect on non-dimensional temperature position of fluid. Also reduced Nusselt is proposed as a measure for the Nusselt number between curved and straight pipe. In creep flow, increasing of Reynolds number leads to decreasing of reduced Nusselt number. But in inertial flow, inverse results will be obtained.