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With the rapid growth of data with different modalities on the Internet, cross-modal retrieval has gradually become a hot research topic. Due to its efficiency and effectiveness, Hashing based methods have become one of the most popular large-scale cross-modal retrieval strategies. In most of the image-text cross-modal retrieval methods, the goal is to make the deep features of the images similar to the corresponding deep text features. However, these methods incorporate background information of the images into the feature learning, as a result, the retrieval performance is decreased. To solve this problem, OFBDH (object feature based deep Hashing) is proposed to learn optimal discriminative maximum activations of convolutions from the feature maps to represent the object features, and then the learned object features are integrated into the image-text cross-modal network learning. Experimental results show that OFBDH can obtain satisfactory cross-modal retrieval results on MIRFLICKR-25K, IAPR TC-12 and NUS-WIDE.