The intrinsic birefringence in drcular-core side-hole fiber is reported. The finite element method is used to build the model,in which the stress distribution and the refractive index distribution in the cross section of the fiber and the birefringence are calculated. The model electric field,the geometrical and stress-induced birefringence are calculated. It is concluded that in circular-core side hole fiber, the geometrical birefringence is dominant. The reason why the stress-induced birefrin gence is minute lies in the special structure of the fiber when the variation of the model electric field distribution and the limiting factor of the power are considered. The birefringence of some other drcular-core side-hole fibers which have different side-hole are also calculated in this paper,and an optimized structure design of the side-hole fiber is drawn.