Based on the eigenvalue equation equation of waveguide for scalar quantity and the recursion relation of its eigen-functions, a kind of theoretical method, by which waveguide dispersion in single mode fiber can be analytically solved by means of the equation called D. Gloge model, is put forward and the analytic solution of the dispersion in single mode fiber is given out. It shows that the analytic method can almost precisely solve dispersion problem of single mode fiber by analysis of a difference between approximate and accurate solution of the normalized transmission constant. Experimental data and calculated curve of the dispersion about general single mode fiber (G.652) is compared and they dovetail very well. By use of the result, the calculating precision of numeric differential method and empirical formula is analyzed.