A wideband high gain three-layer hemispherical dielectric resonator antenna (HDRA) that operates at TE511 and TE711 higher order modes is proposed. The HDRA is composed of three layers, which has permittivities of 20, 10 and 3.5. The multilayer structure has been chosen in order to reduce the Q-factor and achieve a wider impedance bandwidth. Cross slot feeding mechanism has been utilized taking into account the excited higher order modes for gain enhancement. The proposed antenna provides an impedance bandwidth of 35.8% over a frequency range of 20.8 to 29.9 GHz in conjunction with a high gain of ~9.5 dBi. The proposed DRA represents the first attempt in utilizing a mm-wave hemispherical DRA.