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MapReduce has been widely used as a powerful parallel data processing model and is adopted by most cloud providers to build cloud computing framework. However, in open cloud systems, security of computation becomes a great challenge. Moreover, MapReduce data-processing services are long-running, which increases the possibility that an adversary launches an attack on the workers and make them behave maliciously and then tamper with the computation integrity of user tasks where their executions are generally performed in different administration domains out of the user control. Thus, the results of the computation might be erroneous and dishonest. In this paper, we propose a new mechanism based on weighted t-first voting method for ensuring the integrity of MapReduce in open cloud computing environment. Our mechanism can defeat both collusive and non-collusive malicious entities and therefore guarantee high computation accuracy.