As unmanned aerial vehicles (UAVs) are widely used in various fields, there is an increasing demand for UAV anti-jamming, multipath mitigation, and covert secrecy. Frequency-hopping binary offset carrier (FH-BOC) signals possess higher anti-jamming and multipath mitigation capabilities than direct-sequence spread spectrum (DSSS) and binary offset carrier (BOC) signals. A prerequisite for constructing communication links between UAVs using FH-BOC signals is the design of efficient acquisition algorithms to capture the signals successfully. In this paper, the modulation and characteristics of the FH-BOC signal are introduced. The maximum relative velocity between UAVs is 5.5 km/s, the maximum acceleration is 50 g, and the maximum plus acceleration is 20 g/s. In this high dynamic environment, the parameters for the parallel code phase and Partial Matched Filter–Fast Fourier Transform (PMF-FFT) acquisition algorithms targeting FH-BOC(10,1) signals are designed, and the acquisition performance of these algorithms is comparatively analyzed. The acquisition time for the first and second algorithms is 4.3317 s and 6.137 s. The number of real additions required by the first and second algorithms is approximately 10.9×109 and 8.9×109, and the number of real multiplications is approximately 7.6×109 and 6.7×109. This helps in selecting the acquisition algorithm when FH-BOC signals are used to build inter-UAV communication links.