It is well known that the application of the nonlinear coordinate transformations is useful for efficient numerical evaluation of weakly singular integrals. In this paper, we consider the trapezoidal rule combined with a nonlinear transformation $Omega$$_{m}$(b;$chi$), containing a parameter b, proposed first by Yun [14]. It is shown that the trapezoidal rule with the transformation $Omega$$_{m}$(b;$chi$), like the case of the Gauss-Legendre quadrature rule, can improve the asymptotic truncation error by using a moderately large b. By several examples, we compare the numerical results of the present method with those of some existing methods. This shows the superiority of the transformation $Omega$$_{m}$(b;$chi$).TEX>).