In order to extend the application of the fiber couplers and develop the new function of fiber couplers, by utilizing the fused\|taper technology, a fiber coupler sensitive to wavelength is obtained. The couplers can split light beam and simultaneously is sensitive to wavelength. The experimental value agrees with the theoretical value. In experiment, the wavelength sensitivity of the coupler is maximized to be 17.86％/ nm. The coupler sensitive to wavelength is easy to be produced by the fused-taper technology and the peak wavelength of the coupling ratio can be well controlled. The coupler can be used to demodulate wavelength shift of fiber Bragg gratings (FBGs). When the Bragg wavelength of FBG agrees with the maximum sensitivity wavelength, the shift of the Bragg wavelength will influence coupling ratio of the coupler output. FBG with 1566.71 nm Bragg wavelength is demodulated by the self-made coupler. When the shift of wavelength reaches 1.80 nm, the coupling ratio varies about 20.34%. The demodulation system is simple and compatible with fiber device. It can be used in health monitoring for huge buildings.