This paper introduces a new method for constructing approximate solutions to a class of Wiener--Hopf equations. This is particularly useful since exact solutions of this class of Wiener--Hopf equations currently cannot be obtained. The proposed method could be considered as a generalization of the “pole removal” technique and Schwarzschild's series. The criteria for convergence is proved. The error in the approximation is explicitly estimated, and by a sufficient number of iterations it could be made arbitrarily small. Typically only a few iterations are required for practical purposes. The theory is illustrated by numerical examples that demonstrate the advantages of the proposed procedure. This method was motivated by and successfully applied to problems in acoustics.