Multiple connected regions bounded by circles are crucial from the point of view of analyzing physical problems and reducing the amount of computation. However, finding a conformal mapping function that maps a multiple connected region to circular domain is challenging. Koebe’s iterative method provides a theoretically feasible path for the conformal mapping of a multiple connected region to a circular region. In this study, a numerical implementation of Koebe’s iterative method is accomplished using the charge simulation method, and an algorithm for conformal circular mapping of unbounded multiple connected regions is proposed. Through numerical experiments, this paper successfully verifies the effectiveness of the proposed algorithm.