Cloud computing provides an opportunity to users to outsource their data and applications. However, data privacy is one of the key challenges for the users who are outsourcing data on some transparent cloud servers. Data encryption is the best option to protect users' data privacy on the cloud. However, computation overheads of encryption methods could be expensive to some small computing machines, such as mobile or IoT devices with limited resources, such as battery. In our previous study, we developed a light-weight Data Privacy Method (DPM) based on a chaos system that uses a Pseudo Random Permutation (PRP) to scramble the content of original data. Although the nature of PRP is against parallelization, we provide an efficient parallel algorithm to scramble a file while the file splits into multiple chunks. The parallel DPM avoids an adversary to access the original data (e.g., by using a brute-force attack), when the size of each scrambled data is large enough. In this paper, we accelerate DPM on a Graphic Processing Unit (GPU) by using NVIDIA CUDA platform for implementation. We assess the generated shuffle addresses from pseudo-random and the distribution of randomness when the computation on data is parallelized on a multiple GPU-cores. A set of rigorous evaluation results shows that the parallel DPM provides a superior performance over tradition DPM when the most time consuming of native CUDA parallel functions have monitored. We also perform a security analysis of parallel DPM to ensure it is secure and it is a cost effective model to protect users' data privacy in a cloud environment.