  The RF design of a 325MHz {\beta}=0.37 superconducting double spoke cavity
for China ADS has been finished. In this paper, the optimization of the spoke
cavity is described in detail. The main goal in the RF design is to decrease
the normalized surface field. We use the elliptic column instead of cylinder to
decrease the normalized magnetic field. The RF simulation gives the optimum
parameters Ep/Eacc of 4.39 and Bp/Eacc of 7.15mT/(MV/m), which meet the
requirement of C-ADS.
