We mainly discuss the convergence of series of sets in Euclidean space in this paper, and we extend the Dirichlet’s test to the series of sets in Euclidean space. However, the Dirichlet’s test is used to judge the convergence to the form of ΣAnBn. Thus, we must define the addition and the multiplication of series of sets, especially in the multiplication part, which is satisfied with the condition of the same dimension after multiplying. In consequence, it is successfully extended to the convergence of series of sets in Euclidean space, and which is the characteristic and the main result of the paper.