A mathematical expression for two-beam interference fringes crossing graded-index (GRIN) optical fiber is derived. The derived model determines the integrated optical path crossing the core of the GRIN optical fiber. The numerical evolution of the model at different values of the fiber exponent optical parameter $\alpha$ is discussed. The theoretical calculations are verified experimentally using high precision phase-shifting interferometry (PSI). The main advantage of the derived model leads to accurate determination of the propagation optical parameters of GRIN optical fibers.