Superconducting generator provides an effective way to reduce the size, weight and cost of large-scale wind genertors. This paper presents the design of an offshore direct-drive superconducting wind generator (SCWG). It has a stator with low temperature superconducting (LTS) field winding and a rotor with normal copper armature winding. First, the main design specifications and topology of the generator are introduced, and some design considerations on SCWGs are discussed. Then the stator and rotor design of the generator are presented, including electromagnetic design, mechanical design, the rotor forced-air cooling system design and cryogenic and refrigeration system design for the superconducting stator, etc. Finally the weight and cost of the proposed SCWG are estimated and compared with that of a direct-drive permanent-magnet wind generator (PMWG) of the same power. It is found that the proposed SCWG is 46% lighter than the PMWG, while the initial material cost is only about 71% of that of the PMWG.