Abstract: The conceptual design of superconducting booster for HI13 tandem accelerator upgrading project is described in this paper. In order to extend the region of stable and the radioactive ion species with energy higher than Coulomb barrier, a booster following the tandem accelerator is planned to build, which is composed of four quarter wave resonators (QWR) in one cryostat. The design goal of the booster is to have an energy gain of 2 MeV/q, at the optimum β=0.07 and frequency of 108 MHz. The detail results of design and calculation of the phase space matching between tandem and linac are given in the paper also.