Based on the generalized Huygens-Fresnel diffraction integral, the analytic propagation expressions for Lorentz beams passing through first-order axisymmetric optical system are derived. The expressions of the beam-width, Rayleigh distance and divergence angle of Lorentz beam are given, and their transform characteristics in free space are discussed. It is shown that the Rayleigh distance of Lorentz beams is larger than that of Gaussian beam. However, the expansion speed of the beam-width of Lorentz beams is lower than that of Gaussian beams and the far-field divergence angle of Lorentz beams is smaller than that of Gaussian beams. Moreover, the transfrom laws of the above parameters for Lorentz beams are the same as those for Gaussian beams passing through free space.