A new ultra-wide-band(UWB) horn antenna based on the nonradiative dielectric waveguide (NRD-guide) was proposed to solve the problem of UWB antennas, TEM horns for example, generally suffer from large side leakage. The rule of the theoretical selection of its parameters, if NRD-guide is used as the UWB antennas, is studied firstly, then the radiation characteristics for an open-ended NRD-guide are calculated by FDTD (finite-difference time-domain) method.