Covariant lagrangian formulation for free bosonic massless fields of arbitrary mixed-symmetry type in (A)dS_d space-time is presented. The analysis is based on the frame-like formulation of higher-spin field dynamics [1] with higher-spin fields described as p-forms taking values in appropriate modules of the (A)dS_d algebra. The problem of finding free field action is reduced to the analysis of an appropriate differential complex, with the derivation Q associated with the variation of the action. The constructed action exhibits additional gauge symmetries in the flat limit in agreement with the general structure of gauge symmetries for mixed-symmetry fields in Minkowski and (A)dS_d spaces.