A new target solution, the granular waterfall target, is proposed here for a muon collider or a muon-decay neutrino beam facility, especially for the moment which adopts a 15 MW continuous-wave (cw) superconducting linac. Compared to the mercury jet target, the granular waterfall target works by a much simpler mechanism which can operate with a much more powerful beam, which are indicated by the detailed investigations into the heat depositions and the evaluations of the temperature increases for different target concepts. By varying proton beam kinetic energy and the geometrical parameters of the waterfall target, an overall understanding of the figure of merit concerning muon production for this target concept as the target solutions of the long-baseline neutrino factory and the medium-baseline moment is obtained. With 8 GeV beam energy and the optimal geometrical parameters, the influence on muon yield by adopting different beam-target interaction parameters is explored. Studies and discussions of the design details concerning beam dumping are also presented.