Aiming at the defect of local binary pattern (LBP), this paper presents a novel and efficient local second-order derivative descriptor for image texture feature extraction based on local convex-and-concave pattern (LCCP). LCCP encodes local directional second-order derivative feature of texture based on local convex-and-concave characteristic, which can really capture the derivative information of texture than the center symmetric local derivative pattern (CS-LDP) does. The proposed multi-resolution LCCP not only encodes directional derivative information but also constructs spatial relationships in a given local region by bilinear interpolation. Extensions of multi-resolution LCCP based on uniform pattern and weighted pattern have also been discussed. The performance of the proposed LCCP and its extensions are assessed on the biometric recognition and texture classification under different challenges. Each image is divided into several regions from which histogram features are extracted and concatenate into an enhanced feature vector for match. Extensive experiments have validated the effectiveness of LCCP and its extensions.