All-fiber add/drop filter based on fiber-Bragg-grating (FBG) assisted coupler is compact and non-interferometric, which reduces the device's sensitivity to the grating position. By introducing the grating refractive modulation into the evanescent field coupling, the coupled-mode equation of FBG-assisted coupler is obtained and the influences of fiber mismatch on the filter spectra is investigated thoroughly. And a high-quality FBG-assisted filter is achieved by adjusting fiber structure parameters using asymmetric fused taper technology. The experimentally measured results are in good agreement with the numerical calculations.