Noncommutative D-Brane in a Nonconstant NS-NSBField Background

We show that, when the field strength $H$ of the NS-NS $B$ field does not vanish, the coordinates $x$ and momenta $p$ of open string end points satisfy a set of mixed commutation relations among themselves. Identifying $x$ and $p$ with the coordinates and derivatives of the D-brane world volume, we find a new type of noncommutative space which is very different from those associated with a constant $B$ field background.