In order to achieve tunable high-precision filtering and expand communication capacity, this paper presents an innovative filtering system approach that combines dual optical fiber Bragg gratings in cascade with a Sagnac loop. This approach has undergone in-depth analysis and numerical simulation validation using Jones matrix theory. Within the wavelength range of 1554 to 1570 nm, tunability is achieved by adjusting the length difference between the optical fiber arms to introduce Sagnac phase shifts. This design not only increases the number of filtering channels but also reduces the Full Width at Half Height (FWHM).It is worth noting that under the same arm length difference conditions, this system exhibits a significant improvement in precision compared to single optical fiber gratings and Sagnac loop filters. With a power loss of 8 dB, this filtering system allows for an arm length error tolerance of up to 196 nm while providing a more accurate transmission spectrum, making tuning more convenient. This filtering system is easy to implement and widely applicable in dense wavelength division multiplexing (DWDM) systems and the field of optical communication.