Let G be a finite group and $omega$(G) the set of elements orders of G. Denote by h($omega$(G)) the number of isomorphism classes of finite groups H satisfying $omega$(G)=$omega$(H). In this paper, we show that for G=PSL(3, q), h($omega$(G))=1 where q=11, 12, 19, 23, 25 and 27 and h($omega$(G)=2 where q = 17 and 29.