Lightweight block ciphers are normally used in low-power resource-constrained environments, while providing reliable and sufficient security. Therefore, it is important to study the security and reliability of lightweight block ciphers. SKINNY is a new lightweight tweakable block cipher. In this paper, we present an efficient attack scheme for SKINNY-64 based on algebraic fault analysis. The optimal fault injection location is given by analyzing the diffusion of a single-bit fault at different locations during the encryption process. At the same time, by combining the algebraic fault analysis method based on S-box decomposition, the master key can be recovered in an average time of 9 s using one fault. To the best of our knowledge, our proposed attack scheme requires fewer faults, is faster to solve, and has a higher success rate than other existing attack methods.