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We present a coupled-mode analysis of a six-port coupler consisting of three parallel uniform long-period fiber gratings, where a longitudinal offset distance may be introduced between the gratings. In particular, we discuss the effects of the grating coupling coefficient and the evanescent-field coupling between the parallel fibers on the performance of the coupler. Our theoretical results compare well with the experimental data for several typical couplers. The method of analysis together with the numerical illustrations presented in the paper can facilitate the design of this new class of six-port all-fiber wavelength-selective couplers with applications in add/drop multiplexing, signal processing, and broadband filtering.