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The problem of object classification when training and test classes are completely disjoint has recently become very popular in computer vision. To solve such problem, one needs to find common attributes of object and transfer them to use in classifying unseen object classes. Unfortunately, most recent attribute classifiers require the full batch-learning. This harshly prohibits an unseen-objects detection system from being used in online incremental machine such as robotics. This paper introduces a new approach for learning and classifying object's attribute in an online incremental manner. An approach is based on Self-Organizing and Incremental Neural Networks (SOINN). The evaluation has been done with 50-classes animal image dataset (30,000+ images). Comparing to the state-of-the-art method, our proposed approach named AT-SOINN (Attribute Transferring based on SOINN) performs the fast attribute learning, transferring and classification, while retaining high accuracy of attribute classification. Proposing AT-SOINN advances one more step towards online incremental unseen-object detections.