  We show that the Fermi surface (FS) in the antiferromagnetic phase of
BaFe$_2$As$_2$ is composed of one hole and two electron pockets, all of which
are three dimensional and closed, in sharp contrast to the FS observed by
angle-resolved photoemission spectroscopy. Considerations on the carrier
compensation and Sommerfeld coefficient rule out existence of unobserved FS
pockets of significant sizes. A standard band structure calculation reasonably
accounts for the observed FS, despite the overestimated ordered moment. The
mass enhancement, the ratio of the effective mass to the band mass, is 2--3.
