Data inconsistency may exist in relational database. One major problem of data quality in relational database is functional dependency violation. To find out inconsistent data in a relational database, people need to detect the functional dependency violations. It is easy to detect dependency violations in centralized databases via SQL-based techniques, although the detection efficiency is not high. However, it is far more challenging to check inconsistencies in distributed databases, not only data shipment needs to be considered, but also the distribution of detecting tasks is a conundrum. These problems are more prominent with big data. This paper proposes a novel single functional dependency inconsistency detection approach in distributed big data, and provides a cost model of inconsistency detection. To reduce data shipment and response time, distributed data are pretreated based on equivalence class. Considering that the inconsistency detection problem is NP-hard, that is impossible to find an optimal solution in polynomial time, this work provides a 3/2-approximate optimal solution. A multiple functional dependencies detection approach is developed for distributed big data based on the minimal set cover theory. This approach allows detecting multiple functional dependencies violations in parallel after one-time data traversal，and it also incorporates load balancing in the detecting process. Experiments on real-world and generated datasets demonstrate that compared with previous detection methods and Naïve method based on Hadoop framework, the presented approach is more efficient and is scalable on big data.