We study the direct CP asymmetry in B → Xsγ decay in SUSY models with non-universal Aterms. We show that the flavour-dependent phases of the A-terms, unlike the flavour-independent ones, can give rise too large contribution to the CP asymmetry while respecting the experimental bounds on the branching ratio of B → Xsγ decay and the electric dipole moments of the electron and neutron. The CP asymmetry of this decay is predicted to be much larger than the standard model prediction in a wide region of the parameter space. In particular, it can be of order 10 − 15% which can be accessible at B factories.PACS numbers:12.60. Jv, 11.30.Er, Direct CP asymmetry in the inclusive radiative decay B → X s γ is measured by the quantityThe Standard Model (SM) prediction for this asymmetry is very small, less than 1%. Thus, the observation of sizeable asymmetry in the decay B → X s γ would be a clean signal of new physics.The most recent result reported by CLEO collaboration for the CP asummetry in these decays is [1]and it is expected that the measurements of A b→sγ CP will be improved in the next few years at the B-factories.Supersymmetric predictions for A b→sγ CP are strongly dependent on the flavour structure of the soft breaking terms. It was shown that in the universal case, as in the minimal supergravity models, the prediction of the asymmetry is less than 2%, since in this case the electric dipole moments (EDM) of the electron and neutron constrain the SUSY CP-violating phases to be very small [2,3]. Furthermore, it is also known that in this case, one can not get any sizeable SUSY contribution to the CP-violating observables, ε and ε ′ /ε [4][5][6][7]. The impact of flavour structure in the non-degenerate A-terms, which is expected in string inspired models, has been studied [6][7][8]. In these works, it was emphasized that the flavour-dependent SUSY CP-violating phases are not essentially constrained by the EDMs and can lead to large contributions to the observed CP-violating phenomena in the kaon system and, in particular, to the direct CP violation measured by ε ′ /ε.In this letter, we explore the effect of these large flavour-dependent phases on inducing a direct CP violation in B → X s γ decay. We will show that the values of the asymmetry A b→sγ CP in this class of models are much larger than the SM prediction in a wide region of the parameter space allowed by experiments, namely the EDM experimental limits and the bounds on the branching ratio of B → X s γ . The enhancement of A b→sγ CP is due to the important contributions from gluino-mediated diagrams, in this scenario, in addition to the usual chargino and charged Higgs contributions.The effective Hamiltonian for b → sγ decay is given bywhere Q i (µ b ) and C i (µ b ) represent an operator for the ∆B = 1 transition and its Wilson coefficient, respectively, evaluated at the renormalization scale µ b ≃ O(m b ). The relevant operators for b → sγ decay are given byThe expression for the asymmetry A b→sγ CP , corrected to next-to-leading order is given by [9]where...