The purpose of this paper is to prode a sufficient and necessary condition of a class of unique factorization domain Z[√-m]={x＋y√-m｜x,y∈z,m∈N}; The result is explored by means of some properties of theirreducible element in such a ring%利用一类整环Z[√-m]={x＋y√-m｜x,y∈z,m∈N}中不可约元的几个性质，给出了这类整环成为唯一因子分解整环的一个充分必要条件．
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