An increasing amount of face images are being captured, shared, or applied in various applications. These images usually contain lots of sensitive information that may lead to privacy disclosure and misuse problems. Some pioneering works show that face image anonymization is one of the promising solutions. We present an innovative identity (ID) camouflage approach by synthesizing anonymous faces so that both artificial intelligence algorithms and humans are unable to recognize them and misuse them freely. Given a face image, our approach consists of two steps. First, we sample an anonymous ID feature point in the feature space. Then, we synthesize a camouflage face by training an anonymous deep generative adversarial network model. To reduce the risk of re-identification, we optimize our anonymous face generator based on the k-nearest neighbors to make a good balance between anonymity and utility of the original face image. The experimental results over the public dataset have verified the feasibility and state-of-the-art efficacy of our approach.