Algebraic recursion formulas for perturbation calculation of successive order approximate propagation constants of graded-index profile planar optical waveguides are derived by the use of hypervirial theorem (HVT) and Hellmann-Feynman theorem (HFT) in quantum mechanics. Algebraic formulas for calculation of modal field with given approximate value of propagation constant are also presented. Numerical results for several typical examples are given. The merit of the present method is that it can be applied to straightforward calculation of propagation constants and the corresponding modal fields in perturbation order.