Abstract : Nuclear star clusters have been found in 75% of local spiral galaxies. They are very compact and massive and seem to co-evolve with central massive black holes. Their origins are still not very clear. Due to its proximity, the Milky Way nuclear star cluster (MWNSC) is a unique lab to study its stellar populations and star formation histories, which help us to understand how MWNSC formed. However, the sample of previous spectrography observations is small. High and extreme spatial variable extinctions limit the use of color magnitude diagram. Instead, we present a time domain study for the central 5 pc of the Milky Way with a four-year baseline HST/WFC3 observations at the F153M (1.53 micron) band. I will give a comprehensive description of the stellar types and variability types of variable stars detected in our catalog and discuss how they can impact our understanding of the stellar populations and in turn the origin of the MWNSC.