A system of nuclear transmutation is presented in which fission products and transuranics (TRU) are incinerated using 14-MeV neutrons produced by muoncatalyzed fusion (μCF) and a subcritical core composed of fission products and TRU. The 14-MeV neutrons produced by μCF are used to transmute 90Sr (fission product) by the (n,2n) reaction. The outcoming neutrons from the 90Sr cell transmute TRU through fission reactions and 99Tc through (n, γ) reactions. This fission energy is converted into electric energy to supply 4 GeV-25 mA deuteron beam power, which is used to produce μ- mesons. We also evaluate the production of tritium that is consumed as a fuel for μCF. The feasibility of the system was analyzed by the MCNP Monte Carlo neutron transport code. The results show that this system can be subcritical and can transmute fission products and TRU with an incineration half-life of approx.1 yr and that the deuteron beam energy and tritium fuel required to operate the system can be supplied within the system cycle itself.