A topological structure of 10 MW fully superconducting offshore wind turbine synchronous generator (FSWTG) is proposed, which stator and rotor windings are both composed with high temperature superconductors (HTS) in this paper. And an electrical design method is presented, which integrates the generator structure design, calculation analysis, and parameter optimization. It is all completed based on the electrical design method that the basic parameter design and the optimization of the number of poles, the pole pitch and the electrical load of the 10 MW FSWTG. Finally, the different design parameters are compared and analyzed for FSWTG, partial superconducting wind turbine synchronous generators (PSWTG: traditional armature winding + high temperature superconducting field winding) and the traditional wind turbine synchronous generators (WTG). The results show that the FSWTG has higher efficiency, lower weight and smaller size than those.