Targeted adversarial attack, which aims to mislead a model to recognize any image as a target object by imperceptible perturbations, has become a mainstream tool for vulnerability assessment of deep neural networks (DNNs). Since existing targeted attackers only learn to attack known target classes, they cannot generalize well to unknown classes.To tackle this issue, we propose Generalized Adversarial attacKER (GAKer), which is able to construct adversarial examples to any target class. The core idea behind GAKer is to craft a latently infected representation during adversarial example generation. To this end, the extracted latent representations of the target object are first injected into intermediate features of an input image in an adversarial generator. Then, the generator is optimized to ensure visual consistency with the input image while being close to the target object in the feature space. Since the GAKer is class-agnostic yet model-agnostic, it can be regarded as a general tool that not only reveals the vulnerability of more DNNs but also identifies deficiencies of DNNs in a wider range of classes. Extensive experiments have demonstrated the effectiveness of our proposed method in generating adversarial examples for both known and unknown classes. Notably, compared with other generative methods, our method achieves an approximate 14.13% higher attack success rate for unknown classes and an approximate 4.23% higher success rate for known classes.