Transmutation of Minor Actinide (MA) in a well thermalized neutron field was studied. Since MA nuclides have large effective cross sections in the well thermalized neutron field, the transmutation in the well thermalized neutron field has an advantage of high transmutation rate. However, the transmutation rate largely decreases by accumulation of Cm-246 when MA is transmuted only in the well thermalized neutron field for a long period. An acceleration method of burn-up of Cm-246 was studied. High transmutation rate can be obtained by providing a neutron field with high flux in the energy region between 1 and 100eV. Two stage transmutation using the well thermalized neutron field and this field can transmute MA rapidly. The applicability of the Advanced Neutron Source (ANS) to the transmutation of MA was examined for a typical MA with the composition in the high-level waste generated in the conventional PWR. If the ANS is applied without changing the fuel inventory, the amount of MA which corresponds to that produced by a conventional 1,175 MWe PWR in one year can be transmuted by the ANS in one year. Furthermore, the amount of the residual can be reduced to about Ig (10(-5) of the initial MA weight) by continuing the transmutation for 5 years owing to the two stage transmutation.