In this paper, an analytical solution for the second order fluid flow in a curved pipe is presented. Perturbation method is used for solving the governing equations and unlike the previous researches, the second order perturbation terms were considered. Here, an analytical relation for the flow rate was presented and axial velocity, secondary flows, and components of stress field were calculated accurately. Also, based on the solution of second order fluid flow presented in current work and upper convected Maxwell fluid flow obtained in previous studies, the effect of retardation and relaxation times of viscoelastic fluids on flow in curved pipes were investigated. In this article, it was shown that increasing the retardation and relaxation times cause the flow rate enhancement and reduction, respectively, which is one of the main innovations of current study.