Recently, the development of storage and networking technology have made processing tremendous data become real. As a result, the demand of discovering knowledge from the bigdata by using tools such as statistical analysis and data mining become higher. Using MapReduce a software framework introduced by Google in 2004 to implement computations on clusters of commodity computers is an economical solution. However, malicious MapReduce framework or source codes can leak the sensitive data through computation process. Giving user the least privilege on MapReduce-based system can solve the problem. Therefore, in our research, we propose a MapReduce-based computational system limiting the access to system resource by using RBAC and TE. Moreover, noise were added to the output of the Reduce to ensure the computational result can not signal the presence of a sensitive data. Our prototype implementation demonstrates the efficiency of preserving privacy on several cases.