Missing data imputation is a critical challenge in various domains, such as healthcare and finance, where data completeness is vital for accurate analysis. Large language models (LLMs), trained on vast corpora, have shown strong potential in data generation, making them a promising tool for data imputation. However, challenges persist in designing effective prompts for a finetuning-free process and in mitigating biases and uncertainty in LLM outputs. To address these issues, we propose a novel framework, LLM-Forest, which introduces a "forest" of few-shot prompt learning LLM "trees" with their outputs aggregated via confidence-based weighted voting based on LLM self-assessment, inspired by the ensemble learning (Random Forest). This framework is established on a new concept of bipartite information graphs to identify high-quality relevant neighboring entries with both feature and value granularity. Extensive experiments on 9 real-world datasets demonstrate the effectiveness and efficiency of LLM-Forest.