MapReduce is becoming a powerful parallel data processing model and is adopted by many cloud services providers to build cloud computing framework. However, in public cloud systems, several service providers may come from different administration domain out of the user control and may be untrustworthy. Hence, security of MapReduce computation is essential in public cloud systems. Additionally, MapReduce data-processing services are long-running, which increases the possibility that an attacker is able to compromise some workers and make them misbehave to corrupt the integrity of all computations allocated to these workers. Thus, the computation integrity is a major concern for Mapreduce user in public cloud environment. In this paper, we propose a new mechanism to ensure the computation integrity of MapReduce in public cloud computing environment. By using replication-based voting method and reputation-based trust management system, our mechanism can efficiently detect both collusive and non-collusive malicious workers and guarantee high computation accuracy with an acceptable overhead.