With the intensifying competition among countries in lunar and deep-space exploration, the forward communication bands between Earth and the Moon are becoming increasingly congested. Spread-spectrum communication is poised to replace conventional unified-carrier wave systems as the dominant telemetry and tracking technology. Compared with Phase-Shift Keying (PSK) modulation, Gaussian-Filtered Minimum-Shift Keying (GMSK) offers lower transmit sidelobes and higher spectral efficiency, making it a promising alternative to Quadrature Phase-Shift Keying (QPSK) as a communication scheme integrated with spread-spectrum systems. This paper compares the direct-sequence spread-spectrum Gaussian-Filtered Minimum-Shift Keying (DSSS–GMSK) modulation scheme with the widely adopted DSSS–BPSK scheme and demonstrates the advantages of DSSS–GMSK, including higher spectral efficiency and improved signal acquisition performance over a wide Doppler dynamic range. This paper also proposes a deep-space DSSS–GMSK signal acquisition algorithm capable of achieving signal acquisition at a carrier-to-noise density ratio $(C/N_0)$ of 34 dB-Hz over a Doppler range from −350 kHz to +350 kHz, demonstrating the feasibility and potential of DSSS–GMSK. The algorithm requires minimal computational hardware resources, and its feasibility has been verified through simulations. Furthermore, its resistance to false locking is analyzed and discussed.