Under the assumption of weakly graded, the dependences of cut-off frequency of guided modes in graded parabolic index optical fibers on refractive indexes of fiber are investigated. The eigenvalue equation and approximate formula for cut-off frequencies of guided modes are obtained by vector-field-method. A parameter γ, called “permittivity ratio”, is defined, which is a constant determined by three refractive indexes of a fiber. It is shown that the normalized cut-off frequencies depend on γ merely. Actual cut-off frequencies of a parabolic index fiber can be obtained with normalized cut-off frequencies by γ simply, and consequently the definite relations between actual frequencies and normalized ones of the graded index fibers are obtained. The curves of normalized cut-off frequencies varying with γ for several modes are displayed. It is shown that the cut-off frequencies increase with γ monotonously, and the rule of increase of HElm modes is different from that of other modes.