The article presents a dual‐optimized adaptive algorithm based on continuous wavelet transform and derivative precise peak capture is developed for fiber cavity ring‐down spectroscopy. Adaptive spectral signal processing is achieved so that peak selection blindness can be effectively solved. To verify the performance of the dual‐optimized adaptive algorithm, a highly sensitive refractive index sensor using a bandgap fiber‐based linear fiber cavity is demonstrated. The developed dual‐optimized adaptive algorithm is compared with the conventional maximum extraction algorithm, and the results show that the dual‐optimized adaptive algorithm has a better performance in suppressing noise and processing superimposed peaks. A stable enhancement factor of 5 is obtained, indicating that the newly developed dual‐optimized adaptive algorithm can generate a high‐quality cavity ring‐down spectrum for applications including refractive index sensors, biosensors, strain gauges, and pressure sensors. [ABSTRACT FROM AUTHOR]