A new well-type neutron counter that is composed of a double-layered annular tube 3He detector, a polyethylene moderator, and a lead gamma shield has been conceptually designed through an MCNPX simulation. A computer program that generates MCNPX input simulating neutron counter performance has been developed with 28 parameters to describe the geometrical structure of the neutron counter and source position. The neutron counter has been optimized to have 72.0-cm diameter × 68.3-cm height with a double-layered annular tube 3He detector of 50-cm length and 2.5-cm thickness through repeated MCNPX simulation with the computer program. The neutron counting efficiency appeared to be >42.4%, and the spatial variance in the sample cavity of the counter was estimated to be <3% for its available space.