An extended application of a new variational approach with localized functional has been presented to solve three-dimensional magnetostatic field problems with open boundary. The method enables an infinite computing region to be easily discretized by using finite and infinite element regions and makes it possible to transform the computing region into a finite computing region. As shown in the results, the proposed method gives better accuracy in the computation of potentials than the standard finite element method under the same computing efforts. It is therefore concluded that, although the present study examined a relatively simple example, the proposed method appeared to be an effective means for solving three-dimensional magnetic field problems with open boundary.