A synergetic system of a high energy proton accelerator and a spectrum controlled type research reactor is considered to be a main candidate of a future neutron source in Kyoto University Research Reactor Institute (KURRI). A study on a conceptual neutronics design has been performed for an accelerator driven subcritical reactor, which is expected to be a main facility for the joint use program as a substitute of the 5 MW research reactor (KUR). The neutron flux levels in several irradiation or experimental ports in the research reactor were examined through neutronics calculations when the reactor is operated either independently or in combination with the accelerator. In addition, preliminary studies were conducted to get information concerning the neutron pulse shape, the neutron multiplication and the power distribution in the accelerator driven system (ADS).