  We perform the consistent quantization of open string D-brane in non-constant
  NS-NS closed string B field background by directly imposing the worldsheet
conformal symmetry. In addition to the previous noncommutative D-brane
coordinates quantization with constant noncommutative parameter $\theta $, we
obtain a set of constraints on the B field which can be interpreted as a
quantum consistent deformation of a curved noncommutative D-brane.
