This paper presents a relativistic coaxial overmoded surface wave oscillator (SWO) working at the terahertz band in the double-ring metamaterial slow wave structure (SWS). A relativistic electron beam passes through the SWS between the inner and outer rings. A coaxial overmoded SWS made up of metal metamaterial is designed to generate the high-power terahertz wave by increasing the beam-wave interaction efficiency and enlarging the transverse size of the terahertz device. It consists of double rings periodically arrayed along the z-direction, and a coaxial conductor with a radius of 2.4 mm. By its dispersive relation the proposed device is studied, from which we choose the 0.14 THz as the operating frequency of the device. Then the parameters of the geometric structure and the electron beam are optimized; the transitional section for extracting the terahertz signal is designed of the largest propagation coefficient. Particle simulation code UNIPIC is employed to verify the initial expectation and potential advantages. When the beam voltage and current are increasing, the operating frequency of the device remains almost constant, and this is the typical characteristic of the SWO. Particle simulation results show that the coaxial inner conductor has a stable operating mode of double-ring metamaterial SWS and can increase the beam-wave interaction efficiency of the SWO at the terahertz band. For a guiding magnetic field of 2.0 T, with the electron beam of 600 kV and a current of 1.0 kA, a 0.141 THz wave output power of 316.8 MW is obtained.