Capacitance versus voltage (C-V) characteristics of Ge-nanocrystal (NC)-embedded metal-oxide-semiconductor (MOS) capacitors with $HfO_2$ gate material were investigated in this work. The current versus voltage (I-V) curves obtained from Ge-NC-embedded MOS capacitors fabricated with the $NH_3$ annealed $HfO_2$ gate material reveal the reduction of leakage current, compared with those of MOS capacitors fabricated with the $O_2$ annealed $HfO_2$ gate material. The C-V curves of the Ge-NC-embedded MOS capacitor with $HfO_2$ gate material annealed in $NH_3$ ambient exhibit counterclockwise hysteresis loop of about 3.45 V memory window when bias voltage was varied from -10 to + 10 V. The observed hysteresis loop indicates the presence of charge storages in the Ge NCs caused by the Fowler-Nordheim (F-N) tunneling. In addition, capacitance versus time characteristics of Ge-NC-embedded MOS capacitors with $HfO_2$ gate material were analyzed to investigate their retention property.