Signal-of-Opportunity (SOP) positioning based on Low-Earth-Orbit (LEO) constellations has gradually become a research hotspot. Due to their large quantity, wide spectral coverage, and strong signal power, LEO satellite SOP positioning exhibits robust anti-jamming capabilities. However, no in-depth studies have been conducted on their anti-jamming performance, particularly regarding the most common type of interference faced by ground receivers—Periodic Frequency Modulation (PFM) interference. Due to the significant differences in signal characteristics between LEO satellite downlink signals and those of Global Navigation Satellite Systems (GNSSs) based on Medium-Earth-Orbit (MEO) or Geostationary-Earth-Orbit (GEO) satellites, traditional interference suppression techniques cannot be directly applied. This paper proposes a Signal Adaptive Iterative Optimization Resampling (SAIOR) algorithm, which leverages the periodicity of PFM jamming signals and the characteristics of LEO constellation signals. The algorithm enhances the concentration of jamming energy by appropriately resampling the data, thereby reducing the overlap between LEO satellite signals and interference. This approach effectively minimizes the damage to the desired signal during anti-jamming processing. Simulation and experimental results demonstrate that, compared to traditional algorithms, this method can effectively eliminates single/multiple-component PFM interference, improve the interference suppression performance under the conditions of narrow bandwidth and high signal power, and holds a high application value in LEO satellite SOP positioning.