This paper proposes a novel shape descriptor, called the normalized weighted shape context (NWSC), for feature-based object matching. A shape context as a global characterization descriptor can represent the distribution of points in a set with scale and rotation invariance, but the current technology only provides invariance under translation, scale, and rotation transformations. This paper employs the inertia ellipse of a shape so that the proposed NWSC not only maintains good invariance under scale and rotation transformations but also obtains very robust and accurate matching results under affine transformations. Weights are assigned to each bin of the descriptor to measure its distinctiveness in the matching process. Moreover, a refining approach is proposed to eliminate mismatched features for self-calibration based on the NWSC. Practical experiments are carried out to evaluate its performance, and the results demonstrate that it significantly outperforms the standard shape context. The experiments show that the proposed approach enhances the matching accuracy to a great extent.