Pay-as-you-consume, as a new type of cloud computing paradigm, has become increasingly popular since a large number of cloud services are gradually opening up to consumers. It gives consumers a great convenience, where users no longer need to buy their hardware resources, but are confronted with how to deal effectively with data from the cloud. How to improve the performance of the cloud platform as a consumer-centric cloud computing model becomes a critical issue. Existing heterogeneous distributed computing systems provide efficient parallel and high fault tolerant and reliable services, due to its characteristics of managing large-scale clusters. Though the latest cloud computing cluster meets the need for faster job execution, more effective use of computing resources is still a challenge. Presently proposed methods concentrated on improving the execution time of incoming jobs, e.g., shortening the MapReduce (MR) time. In this paper, an adaptive scheme is offered to achieve time and space efficiency in a heterogeneous cloud environment. A dynamic speculative execution strategy on real-time management of cluster resources is presented to optimize the execution time of Map phase, and a prediction model is used for fast prediction of task execution time. Combing the prediction model with a multi-objective optimization algorithm, an adaptive solution to optimize the performance of space-time is obtained. Experimental results depict that the proposed scheme can allocate tasks evenly and improve work efficiency in a heterogeneous cluster(1).