The China Spallation Neutron Source (CSNS), located in Dongguan city, is the country's first and only spallation neutron source. It is also the fourth spallation neutron source in the world. It achieved the design index of 100 kW power in February 2020, and its operation is reliable and efficient. The total beam power will be increased to 500 kW in the CSNS phase II upgrade design, where the linac beam energy will be boosted from 80 MeV to 300 MeV and the peak current intensity will be increased from 15 mA to 50 mA by incorporating a superconducting linear accelerator. The double spoke resonator (DSR) will be used in the energy range of 80 MeV to 165 MeV. In the energy range of 165 MeV to 300 MeV, 6-cell ellipsoidal cavity will be used. DSR has many advantages, such as large velocity acceptance, which allows the spoke cavity to be used for a wider range of velocities, small size, high shunt impedance and a high coupling degree, which allows the production error requirements to be relaxed and the frequency bandwidth to be broadened from neighboring modes, among others. The DSR performance, including electromagnetic properties and machine parameters, was simulated and optimized using CST, COMSOL and other simulation software, and it achieved the requirement of CSNS phase II upgrade project. To improve the operating stability of the cavity, the design focused on minimizing E_p/E_acc.