We investigated the feasibility on the application of a superconducting radio frequency (SRF) niobium cavity to an accelerator-based neutron source for boron neutron capture therapy (BNCT). Neutron source is the key component of BNCT and adopting rf-linac based neutron source realizes a medical care system sufficient to be compact, which can be installed in a hospital and to generate intensive neutron yields that the BNCT requires. However, it is still desirable to improve the efficiency of input power on neutron yields and the achievable accelerate field gradient. SRF accelerator technology potentially allows us to enhance the performance because of its prominent lower ohmic loss and higher sustainable accelerating fields. This paper presents a first feasibility study on the application of a SRF niobium cavity to an accelerator-based neutron source for BNCT, assuming that a superconducting radio frequency quadrupole (SC-RFQ) composed of pure bulk niobium at 4.2 K accelerates the proton/deuteron beams to a beryllium or lithium target for the neutron production of BNCT via $^{7}\mathrm{Li}(\mathrm{p},\mathrm{n})^{7}\mathrm{Be}$, $^{9}\mathrm{Be}(\mathrm{p},\mathrm{n})^{9}\mathrm{B}$, or $^{9}\mathrm{Be}(\mathrm{d},\mathrm{n})^{10}\mathrm{B}$. The following beam parameters were used: beam energy of 2.5 MeV (for Li target)/5 MeV (for Be target), ion source current (50 keV, CW 30 mA), normalized beam emittance of 0.02 cm mrad, and resonance frequency of 325 MHz (for proton)/162.5 MHz (for deuteron). Based on these conditions, we evaluated the feasibility on the following three criteria: comparison of the cooling capacity of the refrigerator to the amount of heat, power consumption of AC, and size of the BNCT system. First, we evaluated the amount of heat generated in a cryomodule by adding the ohmic loss of SC-RFQ ${Q}_{\mathrm{rf}}$, beam losses in SC-RFQ ${Q}_{\mathrm{b}}$, heat penetration into the cryomodule ${Q}_{\mathrm{ext}}$, and beam losses of molecular ion beams and poor quality beams emitted from the ion-source at/near the RFQ entrance ${Q}_{\mathrm{emit}}$. In this study, we typically regarded ${Q}_{\mathrm{ext}}$ as 20 W at 4.2 K and considered a new low-energy beam transport system that can suppress ${Q}_{\mathrm{emit}}$ to 0. In addition, ${Q}_{\mathrm{rf}}$ and ${Q}_{\mathrm{b}}$ were numerically evaluated by beam simulation and electromagnetic calculation. The obtained results revealed that the sum of the heat amounts could be sufficiently suppressed below the typical cooling capacity of a commercially available helium refrigerator. Second, we compared the ac power consumption of BNCT between a conventional and SC-BNCT systems, which indicated that the BNCT system adopting the SRF cavity effectively reduced the ac power consumption of SC-BNCT by almost $1/4$ times. Third, the length of the SC-RFQ could be shortened by adjusting the peak surface E-field, as compared to conventional existing RFQs such as J-PARC, SNS, and IFMIF. Eventually, this study demonstrated that the application of the SRF cavity for the rf-linac-based neutron source of BNCT is feasible, and thus provides a foundation for the future development of design for next-generation BNCT systems.