The coupled mode theory for fiber coupler with dissimilar cores is extended to analyze the coupling phenomena in grating frustrated ones. The theoretical results are agreed well with the experimental results in references. Unlike the Bragg grating alone as reflective element, the main effect of the Bragg grating in the coupler is that it introduces a strong dispersion, making the coupler asynchronous in the spectral band of grating. It is also found that the selective spectra of the Bragg fiber coupler caused by the Bragg grating frustrated in the two dissimilar core fiber have not any sidelobe but have very weak jitters on the spectral side part and strong dips on the spectral stop band.