We propose LLM-Eval, a unified multi-dimensional automatic evaluation method for open-domain conversations with large language models (LLMs). Existing evaluation methods often rely on human annotations, ground-truth responses, or multiple LLM prompts, which can be expensive and time-consuming. To address these issues, we design a single prompt-based evaluation method that leverages a unified evaluation schema to cover multiple dimensions of conversation quality in a single model call. We extensively evaluate the performance of LLM-Eval on various benchmark datasets, demonstrating its effectiveness, efficiency, and adaptability compared to state-of-the-art evaluation methods. Our analysis also highlights the importance of choosing suitable LLMs and decoding strategies for accurate evaluation results. LLM-Eval offers a versatile and robust solution for evaluating open-domain conversation systems, streamlining the evaluation process and providing consistent performance across diverse scenarios.