Changes in the light condition affect the solution of intensity-based digital image correlation algorithms. One natural way to decrease the influence of illumination is to consider the gradients of the image rather than the image itself when building the objective function. In this work, a weighted normalized gradient-based algorithm, is proposed. This algorithm optimizes the sum-of-squared difference between the weighted normalized gradients of the reference and deformed images. Due to the lower sensitivity of the gradient to the illumination variation, this algorithm is more robust and accurate than the intensity-based algorithm in case of illumination variations. Yet, it comes with a higher sensitivity to noise that can be mitigated by designing the relevant weighting and normalization of the image gradient. Numerical results demonstrate that the proposed algorithm gives better results in case of linear/non-linear space-based and non-linear gray value-based illumination variation. The proposed algorithm still performs better than the intensity-based algorithm in case of illumination variations and noisy data provided the images are pre-smoothed with a Gaussian low-pass filter in numerical and experimental examples.