Large Language Models (LLMs) have achieved remarkable breakthroughs. However, the huge number of parameters in LLMs require significant amount of memory storage in inference, which prevents their practical deployment in many applications. To reduce memory storage of LLMs, singular value decomposition (SVD) provides a promising solution to approximate weight matrices for compressing LLMs. In this paper, we take a step further to explore parameter sharing across different layers with SVD to achieve more effective compression for LLMs. Specifically, weight matrices in different layers are decomposed and represented as a linear combination of a set of shared basis vectors and unique coefficients. The types of weight matrices and the layer selection for basis sharing are examined when compressing LLMs to maintain the performance. Comprehensive experiments demonstrate that Basis Sharing outperforms state-of-the-art SVD-based compression approaches and parameter sharing techniques, especially under large compression ratios. Code is available at: https://github.com/TUDa-HWAI/Basis_Sharing