This work presents BAdam, an optimization method that leverages the block coordinate descent framework with Adam as the inner solver. BAdam offers a memory efficient approach to the full parameter finetuning of large language models. We conduct theoretical convergence analysis for BAdam in the deterministic case. Experimentally, we apply BAdam to instruction-tune the Llama 2-7B and Llama 3-8B models using a single RTX3090-24GB GPU. The results confirm BAdam's efficiency in terms of memory and running time. Additionally, the convergence verification indicates that BAdam exhibits superior convergence behavior compared to LoRA. Furthermore, the downstream performance evaluation using the MT-bench shows that BAdam modestly surpasses LoRA and more substantially outperforms LOMO. Finally, we compare BAdam with Adam on a medium-sized task, i.e., finetuning RoBERTa-large on the SuperGLUE benchmark. The results demonstrate that BAdam is capable of narrowing the performance gap with Adam more effectively than LoRA.