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Performance diagnosis is labor intensive in production cloud computing systems. Such systems typically face many real-world challenges, which the existing diagnosis techniques for such distributed systems cannot effectively solve. An efficient, unsupervised diagnosis tool for locating fine-grained performance anomalies is still lacking in production cloud computing systems. This paper proposes CloudDiag to bridge this gap. Combining a statistical technique and a fast matrix recovery algorithm, CloudDiag can efficiently pinpoint fine-grained causes of the performance problems, which does not require any domain-specific knowledge to the target system. CloudDiag has been applied in a practical production cloud computing systems to diagnose performance problems. We demonstrate the effectiveness of CloudDiag in three real-world case studies.