A novel Sagnac interferometer employing an optical fiber grating in its loop is presented. The transmission responses of the loops with uniform Bragg gratings and linearly chirped fiber gratings are calculated. The analytic expressions for the loop with a uniform Bragg grating are given. It is found that the loop of a uniform grating leads to equally spaced bandpasses,while that of a chirped fiber grating leads to unequally spaced band-passes. Such Sagnac loops may find applications in dense wavelength division multiplexing (DWDM) systems and optical fiber sensing. The multiple band-passes filters with 8 and 16 channels are demonstrated experimentally. The experiments verify the results of our analysis.