Characteristics of narrowband and wideband spun fiber circular polarizer were numerically analyzed based on spun fiber coupled-mode theory. Influence on the minimum operation length of the narrowband circular polarizer by such factors as polarization state of the incident light, intrinsic linear birefringence and spin rate of the spun fiber were studied. By use of multi-cladding fiber analysis method, influence on the operation bandwidth of the wideband circular polarizer by the various parameters of the spun fiber was analyzed also. The results show that the minimum operation length of narrowband circular polarizer is dependent on the inherent linear birefringence and the spin rate of the fiber, and is independent on the polarization state of the incident light. Changing the spin rate can adjust the bandwidth of the wideband circular polarizer, and changing the distance between the fiber core and the stress zone can lead the central wavelength of it to change accordingly.