In this study we mainly obtained upper and lower bounds for extreme singular values of an n × n complex matrix. Moreover, as an application of this, we got bounds for extreme singular values of Hilbert and Cauchy-Hankel matrices as in the forms H=(1/(i+j-1))i,j=1n and Hn=[1/(g+(i+j)h)]i, j=1n, respectively. We note that the bounds obtained in this paper are more effective than the bounds presented in the paper [2, Theorem 2]. © 2011 Elsevier Inc. All rights reserved.