High performance AlGaN / GaN high electron mobility transistors with recessed gate have been successfully fabricated on sapphire substrate. The HEMT with 0.5 um gate length exhibited excellent current saturation properties without no kink effect and no current degradation. The maximum extrinsic trans-conductance was as high as 327 mS/mm. Effective electron velocity of the HEMT with 0.5um gate length calculated from intrinsic f(T) (49.7GHz) was as high as 1.56 x 10(7) cm/sec. To our knowledge, this is the fastest value of any GaN-based FETs ever reported. Moreover, the HEMTs with T shape recessed gate of 0.21um gate length was also fabricated and exhibited excellent high frequency performances. A maximum unity current cut-off frequency f(T) of 57 GHz and a maximum oscillation frequency f(max) of 108 GHz were obtained.