This paper describes a novel mu-flux (micro flux) pump using a cryotron-like switch that may be coupled to a high-temperature superconductor (HTS) insert coil of a high-field nuclear magnetic resonance (NMR) magnet. The flux pump is essentially comprised of a single superconducting cryotron-like switch loop that is intermittently open and closed. by magnetic field. There is inherently only small energy dissipation in the switching action because the triggering action of the switch is made magnetically not thermally. The micro flux pump can supply precisely a small amount of current into a superconducting load magnet. The switching is stable and fast because the thermal inertia and the temperature sensitivity of the flux pump are not relevant to the operation. The mu-flux pump can be designed to generate minimum total heat input to liquid helium bath of HTS insert coil of NMR magnet.