In order to update the beam power from 100 kW to 500 kW in the China Spallation neutron source (CSNS) Phase II, one of the important measures is to replace the 80 m long beam transport line between the present 80 MeV linac injector and the rapid cycling synchrotron (RCS) to another kind of acceleration structure. In this paper, we proposed a scheme based on 324 MHz double-spoke superconducting cavities. Unlike the superconducting elliptical cavity and normal conducting coupled cavity linac (CCL) structure, the double-spoke cavity belongs to the TB mode structure and has a smaller transverse dimension compared with that of the TH mode one. It can work at base frequency as the drift tube Linac (DTL) section, so that the cost and complexity of the RF system will be much decreased, and the behaviors of the beam dynamics are also improved significantly because of the low charge density and larger longitudinal acceptance. Furthermore, because of the relatively longer interactive length between the charged particle and the electromagnetic field per cell, it needs relatively less cell numbers and it has larger velocity acceptance compared with the double frequency TH structures. The superconducting section consists of 14 periods, each of which includes 3 superconducting cavities encapsulated in one cryomodule and a doublet in room temperate. The general considerations on cavity and beam dynamics design are discussed and the main results are presented.