This paper presents a method for calculating the dispersion of single mode optical fibers (SMOF) with arbitrary refractive index profiles. The dimensionless parameter called "optical dimension" of the fiber is introduced, from which a new dispersion formula of SMOF is derived. All the parameters in the formula are calculated by the variation-finite element method[1] or with the Sellmeier formula[2]. Using program compiled from this calculation, the dispersion curves of SMOF with power-law refractive index profiles haye been determined at two low-loss windows, and 1.55 μm，and the effects of the refractive index dip at the core center on the dispersion in a step index SMOF have been investigated. The method can also be applied to the investigation of new kinds of optical fibers, and for obtaining significant information for the design, fabrication and measurement of SMOF.