An n-tournament T is called k-strong （l≤k≤n-2）, if every （n+1-k）-subtournament of T is strongly connected. This paper proves that a score vector （s1, s2,..., sn）, where s1≤s2≤...≤sn, is the score vector of some k-strong tournament if and only if min{t1, t2,..., tn-1}≥k, where tf=s1+s2+...+sj-j（j-1）/2, j=1, 2,..., n-1.
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