The electromagnetic optimizations of a superconducting Spoke021 cavity is studied in detail for C-ADS project, in this paper. The cavity model has been parameterized, in order to find the possible maxima or minima of the key electro-magnetic parameters, the parameter sweep is performed. The cavity model has been parameterized. For finding the key electromagnetic feature, the geometric parameter sweep is performed. The physical interpretation for the variation of these electromagnetic parameters has been elaborated. The electromagnetic simulation gives the optimum parameters E_p/E_(acc) of 3.14 and B_p/E_(acc) of 4.77 mT/(MV/m). In addition, the Multipacting(MP) has a great effect on the electromagnetic properties of superconducting Spoke021 cavity. So the MP simulations have been done for this cavity, which shows that there is no MP phenomenon at 10 MV/m accelerator gradient. Therefore, the optimized cavity parameters can satisfy the requirements of the C-ADS project. Finally, the TTF(Transit Time Factor) curve of this cavity is calculated and it shows that this cavity has wide velocity acceptance.