This paper proposes a novel and effective geometric invariant shape representation based on Radon and adaptive stationary wavelet transforms. The proposed representation is invariant to general geometrical transformations. Instead of analyzing shapes directly in the spatial domain, the proposed method extracts shape translation and scale invariant features in radon transform domain by statistical and spectral analysis, and also represents the rotation of the shapes by shifts of the extracted features. The adaptive stationary wavelet transform is then applied to obtain energy signatures in each wavelet channel as the final geometric invariant representation. Experiment results show that the proposed shape representation is invariant to rotation, translation, and/or scale changes for images with complex inner shapes, and outperforms the other existing methods with higher recognition rates.