Cavity ring-down spectroscopy (CRDS) is a highly sensitive molecular absorption spectroscopic technology, which has been widely used in mirror reflectance measurement, atmospheric trace gas detection, molecular precision spectroscopy and other fields. It deduces the intracavity absorption by measuring the rapid variation of the ringdown signal. As a result, detector with high linearity, broad bandwidth and low electrical noise is indispensable. Additionally, owing to the large noise in laser frequency, low laser-to-cavity coupling efficiency is obtained. Consequently, the cavity transmission is faint, which deteriorates the detection sensitivity. Optical feedback can address this problem by locking the laser to the cavity longitudinal mode. Then, the laser frequency noise is suppressed and hence better detection sensitivity is expected. Optical feedback CRDS with V-shape cavity has been widely studied. Compared with Fabry-Perot cavity, this cavity geometry is very sensitive to mechanical vibration and possesses low degree of fineness due to an additional mirror. In this paper, optical feedback linear cavity ring-down spectroscopy based on a Fabry-Perot cavity with a degree of fineness of 7800 is presented. The principle of the combination of optical feedback and linear cavity is explained from the perspective of the light phase, which shows that the reflection will not generate efficient optical feedback if the feedback phase is appropriately controlled and laser to cavity locking can be therefore realized. And then, the factors influencing the stability of ring-down signal are analyzed, including the feedback ratio, the trigger voltage for the ringdown event, and the distance between the light spot and the detector center. The experimental results show that a superior fractional uncertainty of the empty ringdown time of 0.026% can be obtained with a low feedback rate (3% FSR), a high ringdown signal trigger threshold (90% cavity mode amplitude) and superposition of the light spot with the detector center. With Allan variance analysis, the white noise response of 1.6 × 10^–9 cm^–1·Hz^–1/2 and the detection sensitivity of 1.3 × 10^–10 cm^–1 for trace gas detection can be achieved in an integration time of 180 s, corresponding to the lowest CH₄ concentration detection of 0.35 × 10^–9 at 6046.9 cm^–1. This robust spectroscopic technique paves the way for constructing high-sensitive and stable-cavity based instrument for trace gas detection.