Current social bias benchmarks for Large Language Models (LLMs) primarily rely on predefined question formats like multiple-choice, limiting their ability to reflect the complexity and open-ended nature of real-world interactions. To close this gap, we extend an existing dataset BBQ (Parrish et al., 2022) to Open-BBQ, a comprehensive framework to evaluate the social bias of LLMs in open-ended settings by incorporating two additional question categories: fill-in-the-blank and short-answer. Since our new Open-BBQ dataset contains a lot of open-ended responses like sentences and paragraphs, we developed an evaluation process to detect biases from open-ended content by labeling sentences and paragraphs. In addition to this, we also found that existing debiasing methods, such as self-debiasing (Gallegos et al., 2024), have over-correction issues, which make the original correct answers incorrect. In order to solve this issue, we propose Composite Prompting, an In-context Learning (ICL) method combining structured examples with explicit chain-of-thought reasoning to form a unified instruction template for LLMs to explicitly identify content that needs debiasing. Experimental results show that the proposed method significantly reduces the bias for both GPT-3.5 and GPT-4o while maintaining high accuracy.