The receptance function is very important which interrelates the harmonic excitation and the response of a structure in the frequency domain. This report presents the exact formula of receptance function of AFG beam with varying width. When the width of beam decreases from the fixed end to the free end, the natural frequencies of the AFG beam increase. The distributions of materials and the width have significant effect on the vibration amplitude of beam. The vibration amplitude of beam at the free end is much higher than that at peaks of receptance positions of beam when the width decreases from the fixed end toward the free end