An aperiodic fiber grating with asymmetric reflection spectrum structure is studied, and its spectrum characteristics are described by an introduced parameter, the spectrum profile slope, which can measure the spectrum asymmetric property. Based on the fiber gratings with asymmetric reflection spectra, a new sort of tunable narrow band-pass fiber grating filter is designed as its application, whose characteristics, namely working wavelength, band width, and tunable range, are analyzed as well.