We describe the development of antihydrogen beams for the hyperfine spectroscopy of ground-state antihydrogen atoms using a cusp trap in ASACUSA (Atomic Spectroscopy and Collisions Using Slow Antiprotons) experiments. The magnetic field generated by a superconducting anti-Helmholtz coil of the cusp trap is expected to produce spin-polarized antihydrogen beams. Recently, the ASACUSA collaboration succeeded in synthesizing antihydrogen atoms and producing antihydrogen atomic beams from the cusp trap. This is important step to advancing towards precision in-flight spectroscopy of antihydrogen atoms.