Existing Low-Rank Adaptation (LoRA) methods face challenges on sparse Large Language Models (LLMs) due to the inability to maintain sparsity. Recent works introduce methods that maintain sparsity by augmenting LoRA techniques with additional masking mechanisms. Despite these successes, such approaches suffer from an increased memory and computation overhead, which affects the efficiency of LoRA methods. In response to this limitation, we introduce Low Rank adaptation method for Sparse LLM (LoRS), an innovative method designed to achieve both memory and computation efficiency when fine-tuning sparse LLMs. To mitigate the substantial memory and computation demands associated with preserving sparsity, our approach incorporates strategies of weight recomputing and computational graph rearrangement. In addition, we also improve the effectiveness of LoRS through better adapter initialization. These innovations lead to a notable reduction in memory and computation consumption during the fine-tuning phase, while achieving performance levels that outperform existing LoRA approaches.