Pure metallic reflectarray antennas have good power efficiency and low fabrication cost, which were limited to single band operation. A dual-band reflectarray antenna is developed for two directional beams by two feeds. The reflecting elements are metal waveguides, and have novel properties of both resonant and non-resonant modes at the two frequency bands. The low and high frequency bands can be easily separated by the cutoff frequency of waveguide modes. The phase changing mechanisms via ray optics and fundamental waveguide modes, respectively provide simple formulations for elemental structure design of directional beams. Radiation characteristics of the linear and circular polarizations are cross-examined with good performance by full-wave simulations using HFSS, FEKO and CST at 28 and 60 GHz bands for 5G front-haul network applications.