The star µ Orionis is a spectroscopic visual quadruple system in which each visual component is a short-period spectroscopic binary. The visual orbit has a period of 18.644 yr, a high eccentricity of 0.7426, and a high inclination of 96°.2. The visual primary consists of an Am star and probably a G or early K dwarf that orbit each other in a nearly circular orbit with a period of 4.4475858 days. The visual secondary consists of a pair of F5: V stars in a circular orbit with a period of 4.7835361 days. While the masses of the two stars are nearly identical and the magnitude difference between the pair is close to zero, the projected rotational velocities differ by almost a factor of 2. The orbit for the B subsystem is not coplanar with the visual orbit, while that for the A subsystem is probably not coplanar as well. The orbital parallax of 0".02107±0".00018 is more accurate than that obtained from the Hipparcos observations and corresponds to a distance of 47.5±0.4 pc. A comparison with evolutionary tracks indicates that the Am star is near the end of its main-sequence evolution.