High-Temperature superconducting (HTS) generators are being considered as a competitive candidate in large direct-drive (DD) wind turbines because of their features of being lightweight and compact. Normally a large air gap is inevitable in partially HTS generators, sacrificing the torque producing capability. In this paper, multi-phase armature windings for HTS generators are investigated to reduce the air gap length in HTS generators while not compromising generators' performance. Therefore, the torque density of HTS generators can be improved without any added costs. Five different multi-phase armature winding schemes are studied in the paper. Their performance regarding torque production and rotor losses in a 10 MW DD HTS generator are examined. The findings show that employing multi-phase armature windings can reduce the mechanical air gap without generating extra eddy current losses in the rotor, and the torque production can be improved by up to 9.1%. In addition, the alternating magnetic field reaching the HTS field winding are also reduced by using multi-phase armature windings, resulting in lower AC losses and cooling costs.