For Laguerre Gaussian vortex beam, the analytical expression of the electric field is derived in the observation plane after propagation. Theoretical analysis shows that the definition of Gaussian beam is unsuitable to describing the size of the laguerre Gaussian vortex beam while propagation. It is more convenient that the radius of the point where intensity is maximum is used to define the vortex beam after propagation. Besides the beam broadening effect induced by diffraction, phase distribution exhibits special change in the observation plane. Isophase line changes from radial to arc. If the topological charge of the vortex beam is positive, the isophase line will bend clockwise after propagation; if the topological charge of the vortex beam is negative, the isophase line will bend anticlockwise.