Multimodal large language models (MLLMs) have attracted increasing attention in the past few years, but they may still generate descriptions that include objects not present in the corresponding images, a phenomenon known as object hallucination. To eliminate hallucinations, existing methods manually annotate paired responses with and without hallucinations, and then employ various alignment algorithms to improve the alignment capability between images and text. However, they not only demand considerable computation resources during the finetuning stage but also require expensive human annotation to construct paired data needed by the alignment algorithms. To address these issues, we propose an efficient fine-grained unlearning framework (EFUF), which performs gradient ascent utilizing three tailored losses to eliminate hallucinations without paired data. Extensive experiments show that our method consistently reduces hallucinations while preserving the generation quality with modest computational overhead. Our code and datasets will be publicly available.