With the increase of dirty data, data cleaning turns into a crux of data analysis. Most of the existing algorithms rely on either qualitative techniques (e.g., data rules) or quantitative ones (e.g., statistical methods). In this paper, we present a novel hybrid data cleaning framework on top of Markov logic networks (MLNs), termed as MLNClean, which is capable of cleaning both schema-level and instance-level errors. MLNClean mainly consists of two cleaning stages, namely, first cleaning multiple data versions separately (each of which corresponds to one data rule), and then deriving the final clean data based on multiple data versions. Moreover, we propose a series of techniques/concepts, e.g., the MLN index, the concepts of reliability score and fusion score, to facilitate the cleaning process. Extensive experimental results on both real and synthetic datasets demonstrate the superiority of MLNClean to the state-of-the-art approach in terms of both accuracy and efficiency.