The analytical expression of the electric field is derived on the observation plane for vortex beam after propagation. Based on the derived result, the intensity distribution and the beam size on the observation plane is analyzed. Different from the traditional Gaussian beam, there is no generous definition for vortex beam after propagation. The mean-square width and the equivalent-beam width are put forward to investigate the spreading of vortex beam while propagating. It is shown that the spreading of vortex beam depends on the topological charge and propagation length. The beam with bigger topological charge spreads faster. Calculation results reveal that the equivalent beam length is more suitable to describe the beam size of vortex beam after propagation.