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The weapon-target assignment (WTA) problem is intuitively non-linear. In this paper the WTA problem is modelled as an integer linear program (ILP) without lose the problem's exact optimality, and it is proposed that there exists an upper bound of the number of attacking weapons for a specific target (the attack-number bound) providing the solution is optimal. By limiting the attack-number bound, the dimension of the ILP model of the WTA problem can be drastically decreased, and this enables the ILP of the WTA problem can be solved in short time. Computational experiments have been done on data provided by literature published in recent years, and the results show that the method proposed by this paper has clear advances over the traditional methods in both better optimality and faster computational speed. [ABSTRACT FROM AUTHOR]