Recently, for many kinds of complex engineering problems, numerical analysis methods have become very useful with the remarkable development of the digital computer, especially the super computer. I have recently proposed a new method for the vector analysis of the electromagnetic field, which is called as the spatial network method (SNM). This method is based on both the three-dimensional spatial lattice network of Maxwell's equations and the formulation by the Bergeron method in the time domain. For the analysis of some problems involving sources such as currents or charges it is known that the formulation by the vector potential is effective. This paper describes that the SNM can be easily applied to the vector potential fields with the gauge condition in that the divergence of the vector potential is zero. The formulation is performed in the same spatial lattice network as that for Maxwell's equation, and both the magnetic and electric vector potential variables are introduced. Therefore the proposed method succeeds the advantages of SNM for analyses of electromagnetic fields. For examining the fundamental characteristics and the validity of the formulation the electromagnetic field distributions around a line current and a small loop current are computed.