A grating-assisted fiber coupler(GAFC), which consists of a thin-film waveguide with grating and circular optical fiber, is proposed and the optimized power coupling is evaluated by using a technique amenable to rigorous longitudinal modal transmission-line theory(L-MTLT). In addition, novel criteria to couple an optical signal incident through the grating waveguide to a single-mode optical fiber are proposed. The numerical result reveals that the optimized power coupling occurs at minimum-gap condition between rigorous modes rather than for the conventional phase-matching condition.