The design of a W-band traveling-wave tube (TWT) power amplifier based on a groove gap waveguide slow wave circuit is presented in this paper. The technology of gap waveguide is analyzed to aid the design of electromagnetic band gap based slow wave structures in the upper millimeter wave range of the spectrum while alleviating some of the typical fabrication challenges at these frequencies. The results of Particle-In-Cell (PIC) simulations numerically demonstrate a 10-GHz instantaneous 3-dB bandwidth in the range 89-99 GHz with a minimum power gain of 25 dB. A prototype of the complete slow wave structure is manufactured via computer numerical control (CNC) machining and measured to verify the cold simulation results. Machining tolerances and surface roughness are also investigated. The design approach via groove gap waveguide is flexible and can be extended to alternative rectangular waveguide based slow wave structures.