The main intention of this paper is develop a technique for privacy preserving-aware over big data in clouds using variation step size firefly algorithm and MapReduce framework. This paper consists of two phases such as MapReduce phase and evaluation phase. In MapReduce phase, at first we split the big data into a number of maps. After that, we apply the convolution process to the dataset and create a new kernel matrix. Once the convolution process is over, the privacy-persevering framework over big data in cloud systems is performed based on the evaluation phase. In evaluation module, the neural network is trained based on the optimal weight and radial basis function neural network algorithm, which is improving the utility of the privacy data. After that, a MapReduce framework is to protect the private information. Finally, the reduced privacy data are stored in the computer service provider. In this big data experiment, we used census income KDD dataset to evaluate the result.