We propose a new multiplexing technique using amplitude-modulated chirped fiber Bragg gratings that have an identical center Bragg wavelength. Each grating is inscribed with a unique amplitude modulation that allows them to be multiplexed with complete overlapping within a certain bandwidth. To demodulate the multiplexed signal, the discrete wavelet transform is employed. Concurrently, a wavelet denoising technique is used to reduce the noise. This proposed multiplexing technique has been verified through strain measurements. Experimental results showed that for strains applied up to 1250 με the absolute error and cross-talk are within ±20 με and 16 με, respectively. A strain resolution of 4 με is obtained.