As an intense 14-MeV neutron source, a steady-state subignited tokamak plasma is proposed, where a 60-MW neutral beam is injected to sustain a subignited plasma and to drive a plasma current for steady-state operation. Plasma and device parameters are self-consistently designed, taking into account physical (confinement characteristics, beta limit, current drive efficiency, and so on) and engineering (maximum magnetic field strength, blanket/shield thickness, and others) constraints. The result of a comparison between plasmas with A = 2.8 and A = 4 indicates that a large aspect-ratio device is preferable as a neutron source. A surface-averaged 14-MeV neutron flux of ∼0.6 MW/m2 is achievable with R = 4 to 5 m, A = 4, and Bmax = 10 T and is not so sensitive to the major radius. When the maximum magnetic field strength of toroidal field coils is raised to 13 T, a neutron flux more than 1 MW/m2 is available with a device with R = 4 m. If the plasma performance is advanced and plasmas with an L-mode enhancement factor fL of ∼3 and a Troyon coefficient in beta limit g of ∼5 are attainable, a neutron flux of ∼1.6 MW/m2 is achievable even with a device with R = 4 m and Bmax = 10 T. These devices seem to be very attractive not only as a neutron source but also as a supplementary device of an ignition-oriented International Thermonuclear Experimental Reactor (ITER) device.