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Increasingly, individuals and companies adopt a cloud service provider as a primary data and IT infrastructure platform. The remote access of the data inevitably brings the issue of trust. Data encryption is necessary to keep sensitive information secure and private on the cloud. Yet adversaries can still learn valuable information regarding encrypted data by observing data access patterns. To solve such problem, Oblivious RAMs (ORAMs) are proposed to completely hide access patterns. However, most ORAM constructions are expensive and not suitable to deploy in a database for supporting query processing over large data. Furthermore, an ORAM processes queries synchronously, hence, does not provide high throughput for concurrent query processing. In this work, we design a practical oblivious query processing framework to enable efficient query processing over a cloud database. In particular, we focus on processing multiple range and kNN queries asynchronously and concurrently with high throughput. The key idea is to integrate indices into ORAM which leverages a suite of optimization techniques (e.g., oblivious batch processing and caching). The effectiveness and efficiency of our oblivious query processing framework is demonstrated through extensive evaluations over large datasets. Our construction shows an order of magnitude speedup in comparison with other baselines.