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Optical fiber distributed acoustic sensing (DAS) based on phase-sensitive optical time domain reflectometry (φ-OTDR) is in great demand in many long-distance application fields, such as railway and pipeline safety monitoring. However, the DAS measurement distance is limited by the transmission loss of optical fiber and ultralow backscattering power. In this paper, a DAS system based on multispan relay amplification is proposed, where the bidirectional erbium-doped fiber amplifier (EDFA) is designed as a relay module to amplify both the probe light and the backscattering light. In the theoretical noise model, the parameters of our system are carefully analyzed and optimized for a longer sensing distance, including the extinction ratio (ER), span number, span length, and gain of erbium-doped fiber amplifiers. The numerical simulation shows that a bidirectional EDFA relay DAS system can detect signals over 2500 km, as long as the span number is set to be more than 100. To verify the effectiveness of the scheme, a six-span coherent-detection-based DAS system with an optimal design was established, where the cascaded acoustic-optic modulators (AOMs) were used for a high ER of 104 dB. The results demonstrate that the signal at the far end of 300.2 km can be detected and recovered, achieving a high signal-to-noise ratio of 59.6 dB and a high strain resolution of 51.8pε/Hz at 50 Hz with a 20 m spatial resolution. This is, to the best of our knowledge, a superior DAS sensing distance with such a high strain resolution.