We consider the neutralino to be the lightest supersymmetric particle in the framework of the minimal anomaly mediated supersymmetry breaking (mAMSB) model. We have studied the variation of the neutralino mass with the supersymmetric parameters. Considering these neutralinos to be candidates for weakly interacting massive particles (WIMPs) or cold dark matter, we have calculated the neutralino nucleon scalar cross sections and compared them with the results of the DAMA-NaI neutralino direct detection search. From this study, we observe that the mAMSB model results cannot explain the allowed region in WIMP mass and WIMP–nucleon scalar cross-section space obtained from the annual modulation signature in the DAMA-NaI experiment.