In big data applications, data privacy is one of the most concerned issues because processing large-scale privacy-sensitive data sets often requires computation power provided by public cloud services. Sub-tree data anonymization, achieving a good trade-off between data utility and distortion, is a widely adopted scheme to anonymize data sets for privacy preservation. Top-Down Specialization (TDS) and Bottom-Up Generalization (BUG) are two ways to fulfill sub-tree anonymization. However, existing approaches for sub-tree anonymization fall short of parallelization capability, thereby lacking scalability in handling big data on cloud. Still, both TDS and BUG suffer from poor performance for certain value of k-anonymity parameter if they are utilized individually. In this paper, we propose a hybrid approach that combines TDS and BUG together for efficient sub-tree anonymization over big data. Further, we design MapReduce based algorithms for two components (TDS and BUG) to gain high scalability by exploiting powerful computation capability of cloud. Experiment evaluations demonstrate that the hybrid approach significantly improves the scalability and efficiency of sub-tree anonymization scheme over existing approaches.