This paper proposes a distributed acoustic sensor (DAS) scheme, which is immune to the fading problem and can overcome the trade-off existing in traditional ϕ-OTDR between spatial resolution and sensing distance. An optical chirped pulse and non-matched filter method are used, and hence the spatial resolution is mainly determined by the bandwidth of the chirped pulse and non-matched ratio, rather than pulse duration. The Rayleigh interference pattern method is adopted here to quantitatively demodulate strain distribution along the whole sensing fiber, so there is no fading problem, which is a serious problem in the Rayleigh phase method. In proof-of-concept experiments, a DAS with 2-m spatial resolution and 10-km distance range is demonstrated. The response bandwidth of strain is 5 kHz, only limited by the fiber length. A nε-scale strain signal is detected at the far end of fiber with a high SNR of 35 dB.