In this paper， a design， fabrication and cold test of a high efficiency folded groove waveguide （FGW） for w-band （85~110GHz） sheet beam traveling wave tube （TWT） is proposed. One stage phase velocity taper （OSPVT） was used in the FGW to enhance the electronic efficiency of a millimeter-wave sheet beam TWT. The OSPVT was realized via a change of the period of the FGW. Three FGWs with and without OSPVT were fabricated and their measured s-parameters demonstrate good transmission characteristics and wide bandwidth. Moreover， wave dispersions and phase velocities of the unchanged and OSPVT FGWs were obtained from measured transmission phases. 3-D particle-in-cell simulations of beam-wave interaction predicted that the proposed TWT with an OSPVT of twenty half periods could output a saturated power of 240 W at 95 GHz， which is about 70 W higher than the case of without OSPVT. Meanwhile， the application of the OSPVT improves the electronic efficiency in the whole operating frequency range of 85~110 GHz， with a maximum efficiency enhancement of about 47% in the vicinity of 95 GHz.