Current Conditional Functional Dependency (CFD) discovery algorithms always need a well-prepared training dataset. This condition makes them difficult to apply on large and low-quality datasets. To handle the volume issue of big data, we develop the sampling algorithms to obtain a small representative training set. We design the fault-tolerant rule discovery and conflict-resolution algorithms to address the low-quality issue of big data. We also propose parameter selection strategy to ensure the effectiveness of CFD discovery algorithms. Experimental results demonstrate that our method can discover effective CFD rules on billion-tuple data within a reasonable period.