  We study the exclusive (Lambda_b -> \Lambda l^+ l^-) decay in the Appelquist,
Chang, Dobrescu model within one universal extra dimension. We investigate the
sensitivity of the branching ratio, lepton polarization and forward-backward
asymmetry A_{FB} to the compactification parameter (1/R) We obtain that the
branching ratio changed about 50% compared to the SM value, when (1/R=200 GeV)
and zero position of the forward-backward asymmetry is shifted to the left
compared to the SM result. Therefore measurement of the branching ratio of
(Lambda_b -> Lambda l^+ l^-) decay and determination of zero position of A_{FB}
are very useful in looking for new physics in the framework of the UED models.
