A broadband dual-band dual circularly polarized millimeter wave single-fed antenna is designed. The antenna operates in n257(26.5-29.5 GHz) and n260(37.0-40.0 GHz) bands simultaneously. Compared with the traditional circularly polarized antenna, irregular patches stacked up and down are used to realize dual-band dual-circular polarization and improve the isolation of signal reception and transmission. By adding a curved parasitic patch, the antenna extends the axial ratio bandwidth. Rectangular gaps in the metal-frame are used to improve the antenna gain and expand the antenna bandwidth. The measurement results show that the relative impedance (<-10 dB) bandwidth at low frequency and high frequency are 20.4% and 17.0% respectively, and the relative axial ratio (<3 dB) bandwidth of dual-band dual-circular polarization are 14.9% and 11.4% respectively. The antenna bandwidth covers n257 and n260 bands, which can be used for communication between 5G mobile devices and LEO satellites.