This paper presents a generalized equivalent multipole-moment method for calculating three-dimensional Laplacian fields in multi-spherical system. The Greengard & Rokhlin's M2M, M2L, and L2L formulae enable the multipole-moment method to calculate the fields in general arrangement of multi-spheres, which involve exclusive and multi-layered spherical arrangement. We applied this method to electric field calculation in biological structures induced by ELF magnetic fields. The induced electric fields in a three eccentric and exclusive spheres system, which models human head with two eyeballs, are calculated under the application of homogeneous and magnetic-dipole fields. The validity of this method is successfully confirmed by comparing the calculated fields with those by the fast-multipole surface-charge-simulation method.