The rapid development of Low Earth Orbit (LEO) satellite navigation systems requires modulation schemes with strong anti-jamming capabilities, high spectral efficiency, and the ability to achieve precise tracking in high-dynamic environments. Traditional Binary Offset Carrier (BOC) modulation suffers from multi-peak ambiguity, leading to false lock issues. To address this, FH-BOC modulation, which integrates BOC modulationand frequency hopping, significantly improves both anti-jamming performance and spectral efficiency. Against this background, this paper proposes a comprehensive high-dynamic tracking algorithm for FH-BOC signals. (1) Based on the adaptive Kalman filter algorithm, high-precision carrier tracking was achieved in high-dynamic environments. (2) By leveraging the correlation between the ranging code and frequency-hopping offset carrier, a composite pseudo-code is generated through the XOR operation, and a corresponding composite code-tracking loop is introduced. (3) Based on code loop tracking results, the frequency-hopping moments of the subcarrier are detected, and a phase-locked loop for the frequency-hopping subcarrier is established. Simulation results indicate that the algorithm achieves centimeter-level pseudorange measurement accuracy for FH-BOC navigation signals under the JPL high-dynamic model.