The traditional authenticity identification of calligraphy is usually applied in the manner of expert appraisal or spectral analysis. A new authenticity identification method of calligraphy which is based on image shape fidelity is proposed in this paper. The invariant moment applying to the field of pattern recognition is used for the authenticity identification of calligraphy. Seven invariant moments are tested for the performance of shape fidelity, including Hu moment, Zernike moment, Pseudo-Zernike moment, Legendre moment, Fourier-Mellin moment, Tchebichef moment and Krawtchouk moment. The concept of shape fidelity is proposed as the assessment index of the authenticity of calligraphy. The reliability of identification is further guaranteed by the high definition, high precision and high fidelity image acquisition and processing of calligraphies. Experimental results show that our method can recognize the differences in calligraphies which are difficult to distinguish with the naked eyes and can improve the efficiency and credibility of the identification of calligraphies with low cost of identification time and better anti-interference. It has a good significance in the authenticity identification of calligraphy.