We theoretically analyze the linear momentum density and orbital angular momentum (OAM) propagation characteristics of Gaussian vortex beams in free space, and perform detailed numerical simulation analysis of the linear momentum density and OAM propagation characteristics. Further, we study the variation of the propagation characteristics with different topological charges. In addition, we also analyzed the position of momentum in the transverse profile, where the momentum density of the spot will be broadened with propagation distance. This study can provide guidance for using vortex beams in optical communication and manipulation.