To improve the anti-noise ability of the digital image correlation method, we analyze the influence of gray gradient calculation error on the measurement accuracy of the digital image correlation method. An improved algorithm is proposed to calculate the gray gradient of the image by the Tikhonov regularization method and the sub-pixel displacement of the image by the inverse compositional Gauss-Newton (IC-GN) method. On the basis of the numerical simulation of the speckle pattern, the relative calculation error of the gray gradient is studied, and the measurement accuracy of the digital image correlation method is analyzed after calculating the gray gradient of the image by the Tikhonov regularization method. The proposed method is verified by experiments in the noise environment. The results show that the gray gradient has great influence on the measurement accuracy of the digital image correlation method. Meanwhile, the measurement accuracy and the anti-noise ability of the digital image correlation method can be effectively improved by the Tikhonov regularization method.