  We analyze homogeneous, anisotropic cosmology driven by a self-interacting
``massive'' antisymmetric tensor field $B_{\mu\nu}$ which is present in string
theories with D-branes. Time-dependent magnetic $B$ field existing in the early
universe can lead to the Bianchi type I universe. Evolutions of such a tensor
field are solved exactly or numerically in the universe dominated by vacuum
energy, radiation, and $B$ field itself. The matter-like behavior of the $B$
field (dubbed as ``$B$-matter'') ensures that the anisotropy disappears at late
time and thus becomes unobservable in a reasonable cosmological scenario. Such
a feature should be contrasted to the cosmology of the conventional massless
antisymmetric tensor field.
