Lorentz-Gauss beams have been introduced to describe some certain laser sources with high divergence. When the q parameter at the source plane tends to infinity, Lorentz-Gauss beams reduce to be Lorentz beams. Based on the Collins integral formula, an analytical propagation formula of a Lorentz-Gauss beam passing through a paraxial abcd optical system is derived. Within the paraxial framework, the propagation properties of Lorentz-Gauss beam are illustrated with numerical examples. Based on the vectorial Rayleigh-Sommerfeld integral formulae, the analytical propagation equation of a nonparaxial Lorentz-Gauss beam in free space is presented, and the corresponding numerical examples are also given. Moreover, the far field expression and the scalar paraxial result are dealt with as special cases of the general formulae.