The center of the Gaussian beam from solid laser cannot be completely aligned with the center of the spiral phase panel (SPP) while vortex beam is produced by SPP. The projecting beam from the SPP is actually an off-center vortex beam. Based on the diffraction theory, the propagation of off-center vortex beam is investigated. The analytic expressions of the electric field and the intensity are derived in the observation plane while the beam propagates a certain distance. It is shown that the intensity distribution of the beam changes asymmetricly. Besides the spreading, the core of the vortex beam moves while propagating, which is quite different from that of the ideal vortex beam. The magnitude of topological charge determines the spreading of the beam and has no influence on the motion of the vortex core. Furthermore, the sign of the topological charge determines the direction along which the core moves. If the topological charge is positive, the core will move in the tangential direction anticlockwise; if it is negative, the core will move in the tangential direction clockwise, from which the conclusion can provide a guidance for the beam aligning while the vortex beam is detected under the condition of long distance propagation.