The rotation, scale and translation invariance of extracted features have a high significance in image recognition. Local binary pattern (LBP) and LBP-based descriptors have been widely used in image recognition due to feature discrimination and computational efficiency. However, most of the existing LBP-based descriptors have been designed to achieve rotation invariance while fail to achieve scale invariance. Moreover, it is usually difficult to achieve a good trade-off between the feature discrimination and the feature dimension. In this work, a learning 2D co-occurrence LBP termed 2D-LCoLBP is proposed to address these issues. Firstly, a weighted joint histogram is constructed in different neighborhoods and scales of an image to represent the multi-neighborhood and multi-scale LBP (2D-MLBP) and achieve the rotation invariance. A feature learning strategy is then designed to learn the compact and robust descriptor (2D-LCoLBP) from LBP pattern pairs across different scales in the extracted 2D-MLBP to characterize the most stable local structures and achieve the scale invariance, as well as decrease the feature dimension and improve the noise robustness. Finally, a linear SVM classifier is employed for recognition. We applied the proposed 2D-LCoLBP on four image recognition tasks-texture, object, face and food recognition with ten image databases. Experimental results show that 2D-LCoLBP has obviously low feature dimension but outperforms the state-of-the-art LBP-based descriptors in terms of recognition accuracy under noise-free, Gaussian noise and JPEG compression conditions.