Learning from preference feedback is a common practice for aligning large language models (LLMs) with human value. Conventionally, preference data is learned and encoded into a scalar reward model that connects a value head with an LLM to produce a scalar score as preference. However, scalar models lack interpretability and are known to be susceptible to biases in datasets. This paper investigates leveraging LLM itself to learn from such preference data and serve as a judge to address both limitations in one shot. Specifically, we prompt the pre-trained LLM to generate initial judgment pairs with contrastive preference in natural language form. The self-generated contrastive judgment pairs are used to train the LLM-as-a-Judge with Direct Preference Optimization (DPO) and incentivize its reasoning capability as a judge. This proposal of learning the LLMas-a-Judge using self-generated Contrastive judgments (Con-J) ensures natural interpretability through the generated rationales supporting the judgments, and demonstrates higher robustness against bias compared to scalar models. Experimental results show that Con-J outperforms the scalar reward model trained on the same collection of preference data, and outperforms a series of open-source and closed-source generative LLMs. We open-source the training process and model weights of Con-J at https://github.com/YeZiyi1998/Con-J.