The Shanghai high-repetition-rate XFEL and extreme light facility (SHINE) under construction is designed to be one of the most advanced free electron laser (FEL) facilities in the world. The main part of the SHINE facility is an 8 GeV superconducting Linac operating in continuous wave (CW) mode. The Linac consists of sev-enty-five 1.3 GHz and two 3.9 GHz cryomodules. Based on the design and experience of 3.9 GHz cavities in the European X-ray free electron laser (E-XFEL) and the Linac coherent light source-II (LCLS-II) projects, we optimize the SHINE 3.9 GHz cavity design to adapt it for CW mode operation. In this paper, we present a particular redesign of the end group for the SHINE 3.9 GHz superconducting cavity that includes a redesign of the end cell and beam pipe to shift away the potentially troublesome lowest high-order modes (HOMs), a modification of the main coupler antenna, and a tuning of the HOM notch filter to meet the cavity requirements. RF losses calculations on the HOM coupler antennas show that the overheating on the innerconductor at the operating mode is diminished signifi-cantly. Furthermore, we have also studied the HOMs to ensure there are no dangerously trapped modes in the optimized cavity design.