A class of singular integral equations arising from the inverse scattering problem has been investigated. The exact solution of the dominant equations was sought which serves as the first approximation for the solution of the complete integral equation. The asymptotic expansions for the phase angles appearing in the solution were derived in order to reduce the computing time for the solution. Two examples were given to illustrate the accuracy of approximations. The method of successive approximations was used to solve the complete integral equation, and convergence of the sequence was discussed.