Transformer-based Language Models (LMs) achieve remarkable performances on a variety of NLU tasks, but are also prone to generating toxic texts such as insults, threats, and profanities which limit their adaptations to the real-world applications. To overcome this issue, a few text generation approaches aim to detoxify toxic texts with additional LMs or perturbations. However, previous methods require excessive memory, computations, and time which are serious bottlenecks in their real-world application. To address such limitations, we propose an effective yet efficient method for language detoxification using an attribute-discriminative latent space. Specifically, we project the latent space of an original Transformer LM to a discriminative latent space on which the texts are well-separated by their attributes, with the help of a projection block and a discriminator. This allows the LM to control the text generation to be non-toxic with minimal memory and computation overhead. We validate our model, Attribute-Discriminative Language Model (ADLM) on detoxified language and dialogue generation tasks, on which our method significantly outperforms baselines both in performance and efficiency.