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Length dependence of bandwidth for graded-index optical fibers with random-axial profile fluctuations is investigated theoretically in connection with optical equalization in long spliced fibers. Based on the statistical approach, a simple analytical formula is derived on the assumption that the profile fluctuation does not cause mode coupling. At a short distance, the bandwidth has been found to be inversely proportional to square root of distance due to the profile fluctuation. The length dependence presents a remarkable contrast to that of the mode-coupling case showing the same dependence at a long distance.