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Crossing-site selection is affected by a variety of technical factors and tactical factors. The index system of crossing-site selection is setup based on detailed analysis of river crossing operation and its requirements in wartime. A fuzzy matter-element model is built up in view of the fuzziness and incompatibility of the indexes, combining quantitative analysis with qualitative analysis, with quantifying the qualitative indexes by linguistic variables and fuzzy numbers. The grey relational analysis theory is used to calculate the value of index weights, to reduce the subjective randomness. The multi-objective selection problem is transformed into the single-object decision by Euclid approach degree. The example shows that the method is very practical and the result is objective. It provides a new approach to select crossing-sites, and has been successfully used in a military decision support system.