In this paper, distributions on a graded manifold whose underlying manifold is orientable are defined as linear forms on the spaces of sections with compact support of the Berezinian sheaf; here linearity is taken with respect to the natural structure of right module of the Berezinian sheaf. The author first gives a description of distributions on open subsets with graded coordinates and explicitely writes the formula for graded coordinate changes. A global expression in terms of ordinary distributions taking values in quotient of a sheaf of top form-valued differential operators on the Berezinian sheaf is also given. The case of non-orientable underlying manifold is considered in the last section of the paper.