In view of many problems associated with the availability of global navigation satellite system (GNSS) signals in high-altitude space, this paper presents a comprehensive and systematic analysis. First, the coverage and strength characteristics of GNSS signals in high-altitude space (i.e., space above the GNSS constellation) are presented, and the visibility of GNSS signals is evaluated by combining these two factors. Second, the geometric configuration and geometric dilution of precision (GDOP) of visible GNSS satellites are analysed. Then, the Doppler shift range of the GNSS signals is deduced based on the dynamic performance of high-altitude spacecraft. Finally, taking GaoFen-4 (GF-4) as the application object, the availability of GNSS signals is simulated and evaluated. GNSS signals in high-altitude space are generally weak, and the visible GNSS satellites are concentrated in the high-elevation range. The combination of main and side lobe signals and compatibility of multiple constellations can increase the number of visible satellites, improve the geometry configuration, reduce GDOP, and thus improve the availability of GNSS signals. The results of this research can provide technical support for the design and development of GNSS receivers suitable for high-altitude space.