Superconducting (SC) radio-frequency quadrupoles (RFQs) have exhibited outstanding performance in transmitting and accelerating high-current continuous-wave (CW) ion beams. They can complete beam acceleration at a much higher gradient and with much lower power consumption compared with normal conducting (NC) RFQs. In this study, we introduce a novel SC RFQ scheme operating at 162.5 MHz to accelerate 10 mA proton beams from 30 keV to 2.5 MeV. It will be used as a crucial component for a neutron source dedicated to Boron Neutron Capture Therapy (BNCT) and neutron imaging projects. For efficient transmission of proton beams, we selected a relatively high inter-vane voltage of 240 kV, and the beam dynamics design yielded satisfactory results. Subsequently, RF design and multi-physics analysis were carried out to validate the reliability of the design. A 30-centimeter-long cavity was specifically designed for the vertical test and allowed for a thorough evaluation of the performance of the SC RFQ after post-treatments. Additionally, the tuning design of the 30 cm cavity was also carried out.