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We have found an efficient approximation based on a quasi-mode method to analyze radiation-mode coupling in long-period fiber grating (LPFG) devices, and which was deduced by consideration of the best confinement condition of radiation-mode spectra inside an optical fiber. A single-mode representation via the quasi-mode method enables one to solve the radiation-mode-coupling problems analytically, which is the advantage of the method. The numerical accuracy is found to quite acceptable in comparison with the conventional method of the Green-function representation of radiation-modes via numerical computation of the integral. Utilizing the proposed method, we present several numerical examples for radiation-mode coupling problems both in uniform and nonuniform LPFGs.