Fine-grained image classification is to recognize hundreds of subcategories belonging to the same basic-level category, such as 200 subcategories belonging to bird, and highly challenging due to large variance in same subcategory and small variance among different subcategories. Existing methods generally find where the object or its parts are and then discriminate which subcategory the image belongs to. However, they mainly have two limitations: (1) Relying on object or parts annotations which are heavily labor consuming. (2) Ignoring the spatial relationship between the object and its parts as well as among these parts, both of which are significantly helpful for finding discriminative parts. Therefore, this paper proposes the object-part attention driven discriminative localization (OPADDL) approach for weakly supervised fine-grained image classification, and the main novelties are: (1) Object-part attention model integrates two level attentions: object-level attention localizes objects of images, and part-level attention selects discriminative parts of object. Both are jointly employed to learn multi-view and multi-scale features to enhance their mutual promotion. (2) Object-part spatial model combines two spatial constraints: object spatial constraint ensures selected parts highly representative, and part spatial constraint eliminates redundancy and enhances discrimination of selected parts. Both are jointly employed to exploit the subtle and local differences for distinguishing the subcategories. Importantly, neither objects nor parts annotations are used, which avoids the heavy labor consuming of labeling. Comparing with more than 10 state-of-the-art methods on 3 widely used datasets, our OPADDL approach achieves the best performance.