  We study the inclusive rare decay $B\to X_d+\gamma$ in the supergravity
inspired Minimal Supersymmetric Standard Model and compute the CP-asymmetry in
the decay rates. We show that there exist two phenomenologically acceptable
sets of SUSY parameters: for one set the CP-asymmetry has the same (positive)
sign as in the Standard Model and lies in the range (5-45)% while for the other
set it is negative with values within -(2-21)%.
