A hexagonal ferrite magnetic powder having an average tabular diameter of from 15 to 30 nm, a coercive force (Hc) of from 2,000 to 5,000 Oe (from 160 to 400 kA/m) and a saturated magnetization (σs) of equal to or more than [the average tabular diameter (nm)×0.37+45] A·m2/kg. This magnetic powder is obtained by melting a starting material containing a material which has a composition within the hatched region (1) in the triangular phase diagram shown in FIG. 1 and quenching the molten product to obtain an amorphous product, subjecting the amorphous product to a thermal treatment, acid treatment, and washing. Also, a magnetic recording medium is obtained by adding this magnetic powder to the magnetic layer and coating it on the support.