Excitation of a linear impedance antenna is considered in a unlimited circular wave-guide. The antenna is located in the waveguide axis and is excited by the relativistic point charge scattered at the antenna end-wall. The electric current distribution and the charge linear density distribution along the antenna are calculated. The delta-shaped re-presentation of a current on one of the antenna ends at the initial instant of time is given. The Green's function of an unlimited circular waveguide, and also the direct and inverse Fourier transform in time domain are used.