To solve the cross-sensitivity problem in the dual-parameter optical fiber system, a new type of sensor based on cascaded interference structure is proposed without cross-sensitivity. The design consists of a Michelson interferometer and a Sagnac interferometer based on a high-birefringence suspended core fiber segment. After calculating by the analogous Fast Fourier Transformation (FFT) and filtering by FFT filter, the spectrum of the sensor responds linearly to the change of axial strain and lateral stress. The sensitivity to lateral stress is 3.13 nm/(kPa) in the range from 0 to 1200 Pa and the axial strain is 1.846e-4 (nm·µɛ)-1 from 0 to 4000 µɛ. The capability of the proposed sensor for dual-parameter sensing is also experimentally demonstrated. The precision rate for dual-parameter sensing is as high as 66.7%, reflecting the sensor's usability for simultaneous measurement of axial strain and lateral stress.