The observed rapid cooling of the neutron star (NS) located at the center of the supernova remnant Cassiopeia A (Cas A) can be explained in the minimal NS cooling scenario. This consequence may be changed if there exists an extra cooling source, such as axion emission. In this talk, I will first give a brief review on the standard NS cooling theory. I will then discuss the Cas A NS cooling in the presence of axion emission. It turns out that we can obtain a lower limit on the axion decay constant from the Cas A NS cooling observation, which is as strong as existing limits set by other astrophysical observations such as SN1987A. I will also talk about some recent progress on the limits on the axion decay constant from NS surface temperature observations.