A number of lens antennas with single-dielectric phase-correcting Fresnel zone plate (FZP) lenses have been designed and studied numerically at microwave and terahertz frequencies, and contrasted to a similar in size and parameters ordinary refractive lens antenna. In a confined frequency band the terahertz grooved-dielectric FZP lenses/antennas with four or more phase-correction steps have gain, beamwidth, crosspolar isolation and input-mismatch comparable to those of the corresponding ordinary lens antenna. An examined 1.5-THz FZP lens antenna designed according to the here-proposed correction in FZP design equation can prevail in gain the ordinary lens antenna, but this finding is not valid for the examined 38-GHz (microwave) FZP lens antenna. Thus, the terahertz FZP lenses are thinner, lighter and effective options to the similar in diameter, focal length and building material ordinary lens for lens antennas construction.