Shape is a very important visual and semantic feature used to describe image, and it can be revealed by image pixels' regional distribution. To binary image, this paper proposes a region-based shape representation, a new "density distribution feature (DDF)", which uses a two-dimensional matrix to express the dimensional distribution information of the object's pixels within binary image. When matching the similarity, we first use the Gaussian model to normalize the two dimensional feature vectors, then integrate them to calculate similarity distance. The experiments results show that this shape feature can depict image well and is invariant to translation, scale and rotation. The paper also evaluates the effectiveness of the proposed descriptor with respect to moment invariants