We are working on designing a next-generation muon facility for LANSCE at Los Alamos National Laboratory. The use of muon accelerators is the key feature to generate a muon micro beam of tunable energy. The muon micro beam will realize a beam luminocity of 10(9) mu(+)/cm(2)s which is 4 orders or more higher than present muon facilities. Some designs and results of simulations, especially a high-collection muon radio-frequency quadrupole, are described in this paper.