On-line analytical processing (OLAP) provides analysis of multi-dimensional data stored in a database and achieves great success in many applications such as sales, marketing, financial data analysis. OLAP operation is a dominant part of data analysis especially when addressing a large amount of data. With the emergence of the MapReduce paradigm and cloud technology, OLAP operation can be processed on big data that resides in scalable, distributed storage. However, current MapReduce implementations of OLAP operation processing have a major performance drawback caused by improper processing procedure. This is crucial when dimension or dependent attributes are large, which is a common case for most data warehouses hold nowadays. To solve this issue, this paper proposes a methodology to accelerate the performance of OLAP operation processing on big data. We have conducted the experiments on the basic algebra of OLAP operation with different data sizes to demonstrate the effectiveness of our system.