Fine-grained image classification is to recognize hundreds of subcategories belonging to the same basic-level category, such as 200 subcategories belonging to the bird, which is highly challenging due to large variance in the same subcategory and small variance among different subcategories. Existing methods generally first locate the objects or parts and then discriminate which subcategory the image belongs to. However, they mainly have two limitations: 1) relying on object or part annotations which are heavily labor consuming; and 2) ignoring the spatial relationships 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 model (OPAM) 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; and 2) Object-part spatial constraint 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 object nor part annotations are used in our proposed approach, which avoids the heavy labor consumption of labeling. Compared with more than ten state-of-the-art methods on four widely-used datasets, our OPAM approach achieves the best performance.