An oversized mode-selective relativistic backward wave oscillator is proposed. This device operates using the pure TM02 mode in the beam-wave interaction area and transmits a pure TM01 mode in the output waveguide. In the beam-wave interaction area, mode selection is well realized through oversized slow-wave structures with a coaxial inner conductor that provides perfect boundary conditions for the TM02 mode and simultaneously eliminates other modes. A large proportion of the TM02 mode field is eventually exported into the output waveguide in the form of a pure TM01 mode. With the large diameter and high mode purity, the device can be expected to have high power capacity. With a 770 kV, 11.0 kA beam guided by a 3.5 T magnetic field, a 3.2 GW microwave at 9.42 GHz has been obtained in our simulation. The device efficiency is 38%.