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A nine-cell superconducting RF accelerating cavity is designed for the TeV electron linear accelerator collider in the next century. The ratio of the maximum surface electric field to the accelerating gradient, Epk/Eac, is reduced to 2.024 and the cell-to-cell coupling remains as high as 1.95%. The distribution of the higher-order mode passbands is reasonable. There is no overlap between these bands, therefore no trapped modes. The circle-straight/line-ellipse-type structure provides good mechanical strength in the accelerating cavity. According to the present state of the art of surface processing techniques of niobium cavities, it is possible to reach an accelerating gradient of 25-30 MV/m with beam load.