The transmission spectrum of one-dimensional (1D) photonic crystal (PC) with positive-negative index alternant multilayer is studied with transfer-matrix method. The result reveals that this type of 1D PC has broad-flat forbidden band and narrow-sharp transmitted band. The transmission-spectrum character is affected by Bragg scattering, Fabry-Pérot resonating and the =0 forbidden band. The position of transmitted band is determined by Fabry-Pérot resonating. A new narrow-band interleaver applied to dense wavelength division multiplexing (DWDM) system is designed by this type of one-dimensional photonic crystal. The simulation result of 0.8 nm channel spacing interleaver is presented. It is shown that this new interleaver has narrow channel spacing, flat forbidden band and narrow transmitted band. The channel spacing can be adjusted by change of the unit period optical thickness of one-dimensional photonic crystal.