As semiconductor technologies progress, testing of small delay defects are becoming more important for SoCs. However, fault diagnosis of small delay defects has not been developed. We propose a novel timing-aware method for diagnosing small delay defects with a small computation cost using gate delay fault simulation with the minimum detectable delay, as introduced in the statistical delay quality model. The experimental results show that the proposed method is capable of identifying fault locations for small delay defects with a small computation cost.