Straggler task detection is one of the main challenges in applying MapReduce for parallelizing and distributing large-scale data processing. It is defined as detecting running tasks on weak nodes. Considering two stages in the Map phase copy, combine and three stages of Reduce shuffle, sort and reduce, the total execution time is the total sum of the execution time of these five stages. Estimating the correct execution time in each stage that results in correct total execution time is the primary purpose of this paper. The proposed method is based on the application of a backpropagation Neural Network NN on the Hadoop for the detection of straggler tasks, to estimate the remaining execution time of tasks that is very important in straggler task detection. Results achieved have been compared with popular algorithms in this domain such as LATE, ESAMR and the real remaining time for WordCount and Sort benchmarks, and shown able to detect straggler tasks and estimate execution time accurately. Besides, it supports to accelerate task execution time.