An iterative domain decomposition method is proposed for numerical analysis of three-dimensional linear magnetostatic problems taking the magnetic vector potential as an unknown function.  The iterative domain decomposition method is combined with the Preconditioned Conjugate Gradient (PCG) procedure and the Hierarchical Domain Decomposition Method (HDDM) which is adopted in parallel computing.  Our previously employed preconditioner was the Neumann-Neumann (NN) preconditioner.  Numerical results showed that the method was only effective for smaller problems.  In this talk, we consider its improvement with the Balancing Domain Decomposition DIAGonal scaling (BDD-DIAG) preconditioner by the fourth author.