In this paper we propose a novel texture descriptor called Fractal Weighted Local Binary Pattern (FWLBP). The fractal dimension (FD) measure is relatively invariant to scale-changes, and presents a good correlation with human viewpoint of surface roughness. We have utilized this property to construct a scale-invariant descriptor. Here, the input image is sampled using an augmented form of the local binary pattern (LBP) over three different radii, and then used an indexing operation to assign FD weights to the collected samples. The final histogram of the descriptor has its features calculated using LBP, and its weights computed from the FD image. The proposed descriptor is scale invariant, and is also robust in rotation or reflection, and partially tolerant to noise and illumination changes. In addition, the local fractal dimension is relatively insensitive to the bi-Lipschitz transformations, whereas its extension is adequate to precisely discriminate the fundamental of texture primitives. Experiment results carried out on standard texture databases show that the proposed descriptor achieved better classification rates compared to the state-of-the-art descriptors.