A phase demodulation method for quasi-distributed acoustic sensing (DAS) systems based on a dual-identical-chirped-pulse and weak fiber Bragg gratings (WFBGs) is proposed. Compared to the use of Rayleigh backscattering light in optical fibers, the implementation of WFBGs can contribute to obtaining an optical signal with a higher signal-to-noise ratio (SNR). The dual-identical-chirped-pulse is generated by a time-delay fiber, and the sinusoidal carrier is generated by the interference between the two chirped pulses reflected by adjacent WFBGs. The phase of the sinusoidal carrier represents the dynamic strain change posed on the sensing fiber. Discrete Fourier transform is used to directly retrieve the phase information. The performance of the phase demodulation from interference signals under different sinusoidal carrier frequencies and SNRs is numerically investigated. The piezoelectric transducer is employed to emulate the sound in the experiment to verify the effectiveness of our method. It is shown that the dynamic strain can be well reconstructed at the end of a 101.64 km fiber when the signal SNR is down to 3.234 dB. Our proposed method enables the application of the long-distance sensing in quasi-DAS systems.