We maimly discuss the convergence of series of sets in the complex space under the Hausdorff distance in this paper. And we extend the Abel’s test to the series of sets. The convergence on Abel’s test is considering ΣAnBn. Therefore, we must define the addition and multiplication of series of sets, which is a natural definition in the complex plane. We also succeeded in applying Abel’s test to the series of sets in the complex plane. This is also the main contribution in this paper.