How far is the closest star to the moon besides the sun?

Alpha Centauri That star is the closest to any planet or dwarf planet in the solar system.

Alpha Centauri had long been considered the closest other star, but it turns out that there is red dwarf star called Proxima Centauri which is fractionally closer. Alpha is a star much like our own Sun, and easily seen in the southern hemisphere. Proxima is, I believe, not visible without a telescope.