The purpose of this work is to demonstrate the quasi-phase-matching of third harmonic generation process in optical fibers using refractive-index gratings. We compare conversion efficiency calculated with analytical coupled modes theory and numerical approach employing system of coupled generalized nonlinear Schrödinger equation. Moreover, we show that introducing the phase matching condition that takes into account the nonlinear contribution to propagation constants significantly increases the conversion efficiency by several orders of magnitude. Finally we optimize the grating constant to maximize conversion efficiency.