The establishment of a scientific and comprehensive comprehensive evaluation model of logistics performance is of great significance to enhance the cost reduction and efficiency of enterprises and market competitiveness. The research constructs a supply chain and logistics performance evaluation model based on supply chain management and logistics performance and performance evaluation with the help of a balanced scorecard, hierarchical analysis method, and fuzzy comprehensive evaluation method. The supply chain and logistics performance evaluation index system is then weighed and analyzed. The experimental object for investigating the evaluation effect of the constructed supply chain and logistics performance evaluation index system is Y Logistics Company. In the proposed supply chain and logistics performance evaluation index system, the weight of internal operation and customer dimension accounts for 61.2%. Y Express Company’s logistics performance evaluation from 2016 to 2020 shows a steady increase. The increase in customer dimension from 1.54 in 2016 to 9.47 in 2020 was the biggest increase among all indicators. Finally, Company Y performs better in the customer dimension, financial dimension, and internal operation, and its indicators of learning and development and social responsibility score lower. Company Y should increase its logistics digital learning and technological innovation and take the initiative to assume social responsibility.