Based on the paraxial approximation of propagation of optical beam, the analytical expression of electric field is derived on the observation plane for the Gaussian beam passing through spiral phase plate (SPP). Based on the derived result, the intensity and phase distributions of the generated Gaussian vortex beam by SPP are analyzed. It is found that, different from the case of ideal SPP, the intensity of the beam from multi-level SPP is periodically distributed in the azimuthal direction. The periodicity is equal to the order of the SPP. A suitable choice of the SPP is 16-level structure to obtain good quality of intensity and phase distributions of the generated vortex beam. On the same condition, obtaining good quality of phase distribution requires longer propagation distance of the beam after SPP. In addition, the topological charge decided by the SPP has almost no influence on the above points. The decisive element is still the order of the SPP. The results can provide guidance on the use of SPP in the experiment.