The imaging performance of spiral zone plates is studied. Spiral zone plate is a new imaging optic device which can implement optical Hilbert transform and produce the edge-enhanced imaging of an object,is presented. The performance of spiral zone plates is numerically analyzed using fast Fourier transform and the working condition of spiral zone plates is studied by the numerical calculation. It is generally considered that the distance between the object and the optics should meet the Fraunhofer diffraction using the spiral zone plate as the spatial filter. The numerical analysis shows that the spiral zone plate still works well in some Fresnel diffraction region. It means that the actual field of view is larger than that restricted by the Fraunhofer diffraction. The experimental results show good agreements with theoretical simulation. The method of fast Fourier transform can effectively evaluate the imaging performance of spiral zone plates and provide an important guide to the design of the spiral zone plate microscope.