Mercury does not have any moons. While moons have been observed on most other planets in the solar system, none has been found orbiting Mercury.
It is believed that if a moon ever did orbit Mercury, that it drifted away or was destroyed or removed by another object. Other planets in the solar system have moons; for example, Mars has two moons, Phobos and Deimos, which are asteroids that were captured under the planet's gravitational force. In the early 1970s, there was a brief period of radiation coming from Mercury that suggested a moon was present, but the radiation quickly vanished.