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Traditional Deep Neural Network (DNN) security is mostly related to the well-known adversarial input example attack. Recently, another dimension of adversarial attack, namely, attack on DNN weight parameters, has been shown to be very powerful. As a representative one, the Bit-Flip-based adversarial weight Attack (BFA) injects an extremely small amount of faults into weight parameters to hijack the executing DNN function. Prior works of BFA focus on un-targeted attack that can hack all inputs into a random output class by flipping a very small number of weight bits stored in computer memory. This paper proposes the first work of targeted BFA based (T-BFA) adversarial weight attack on DNNs, which can intentionally mislead selected inputs to a target output class. The objective is achieved by identifying the weight bits that are highly associated with classification of a targeted output through a class-dependent weight bit ranking algorithm. Our proposed T-BFA performance is successfully demonstrated on multiple DNN architectures for image classification tasks. For example, by merely flipping 27 out of 88 million weight bits of ResNet-18, our T-BFA can misclassify all the images from 'Hen' class into 'Goose' class (i.e., 100 % attack success rate) in ImageNet dataset, while maintaining 59.35 % validation accuracy. Moreover, we successfully demonstrate our T-BFA attack in a real computer prototype system running DNN computation, with Ivy Bridge-based Intel i7 CPU and 8GB DDR3 memory.