In digital image correlation method,the gray value of sub-pixel in speckle pattern is usually obtained by cubic spline interpolation in traditional Newton-Raphson algorithm.Among interpolation algorithms,the cubic Hermite interpolation algorithm has better smoothness.Therefore,a sub-pixel displacement estimation algorithm based on Hermite interpolation was proposed to improve the computation accuracy of traditional Newton-Raphson algorithm.The Hermite interpolation was used to reconstruct the gray value of sub-pixel in this algorithm.The first-order gray gradient was calculated by using Barron operator.Then,the Newton iteration algorithm was employed to compute the sub-pixel displacement.Numerical deformation experiment of real speckle patterns was conducted to verify the effectiveness and calculation accuracy of the proposed algorithm.The results show that the proposed algorithm is used to improve the calculation accuracy of the traditional N-R algorithm effectively and has good stability.