We construct a quadrature rule of interpolatory-type based on a trigonometric interpolation for Cauchy integrals. We obtain the same error bound O(\a(N)(N)\) as Hasegawa and Torii (Math. Comp. 56 (1991) 741-754). Numerical examples are included to substantiate the performance of the present method. (C) 2000 Elsevier Science B.V. All rights reserved.