Large language models (LLMs) hold great promise in summarizing medical evidence. Most recent studies focus on the application of proprietary LLMs. Using proprietary LLMs introduces multiple risk factors, including a lack of transparency and vendor dependency. While open-source LLMs allow better transparency and customization, their performance falls short compared to the proprietary ones. In this study, we investigated to what extent fine-tuning open-source LLMs can further improve their performance. Utilizing a benchmark dataset, MedReview, consisting of 8161 pairs of systematic reviews and summaries, we fine-tuned three broadly-used, open-sourced LLMs, namely PRIMERA, LongT5, and Llama-2. Overall, the performance of open-source models was all improved after fine-tuning. The performance of fine-tuned LongT5 is close to GPT-3.5 with zero-shot settings. Furthermore, smaller fine-tuned models sometimes even demonstrated superior performance compared to larger zero-shot models. The above trends of improvement were manifested in both a human evaluation and a larger-scale GPT4-simulated evaluation.