Image gradient has always been a robust characteristic of digital image which possesses localised spatial information of each pixel in all the directions. Exploiting the gradient information at the pixel level is a good old technique applied in various fields of digital image processing. In this paper, the magnitude and direction of image gradient is explored to design a local descriptor. We propose a novel local feature descriptor based on Complex Gradient Function (CGF), which maps each pixel from the spatial plane into its complex extension involving the magnitude and direction of image gradient at that pixel. We exploit the proposed descriptor for human action recognition from depth sequences and human authentication using iris biometrics. The efficiency of descriptor is demonstrated with experimental results on benchmark datasets IITDelhi, MMU-v2, CASIA-Iris, UBIRIS, and MICHE-I for iris authentication and MSR Action 3D dataset for human action recognition (HAR).