Methane hydrate is a clathrate compound consisting of host cages formed by hydrogen-bonded water molecules and guest molecules or atoms included in the cages. It is thought to be an important constituent of icy planets and their moons which mainly consist of water, methane and ammonia. In particular, recent studies suggest that methane hydrate may be present in significant amounts in the interior of Titan, which is likely an essential source of the methane-rich atmosphere at the surface [e.g., Loveday et al. (2001); Choukroun et al. (2010)]. However, the stability of methane hydrate in water-methane-ammonia system under high-pressure and high-temperature corresponding to the internal conditions of Titan have been still unknown. Therefore, in this study, we report a high-pressure and high-temperature investigation of the stability of methane hydrate in water-methane-ammonia system using X-ray diffraction and Raman spectroscopy combined with externally heated diamond anvil cell.  X-ray diffraction studies revealed that methane hydrate in water-methane-ammonia system transforms from sI cage structure into sH cage structure at approximately 0.8 GPa at room temperature, and further transforms into a filled-ice Ih structure at approximately 1.8 GPa without decomposition into water ice and solid methane. These transition pressures at room temperature were same as those reported for pure methane hydrate [Hirai et al. (2001); Loveday et al. (2001); Shimizu et al. (2002)]. At higher temperature, the melting temperatures for the sI and sH cage structures below 1.8 GPa determined by in situ Raman spectroscopy were good agreement with those of pure methane hydrate reported by previous studies [Dyadin et al. (1997); Bezacier et al. (2014)]. On the other hand, the decomposition temperatures of filled-ice Ih above 1.8 GPa were about 10-20 K lower than those of water-methane system reported by Kadobayashi et al. (2018). Our results suggest that ammonia has a potential to vary the stability of filled-ice Ih of methane hydrate in the interiors of icy moons. Finally, we briefly discuss the implications of our new results for the fate of methane hydrate in concerned with a source of atmospheric methane in Titan.