Mobile device users are involved in social networking, gaming, learning, and even some office work, so the end users expect mobile devices with highresponse computing capacities, storage, and high battery power consumption. The data-intensive applications, such as text search, online gaming, and face recognition usage, have tremendously increased. With such high complex applications, there are many issues in mobile devices, namely, fast battery draining, limited power, low storage capacity, and increased energy consumption. The novelty of this work is to strike a balance between time and energy consumption of mobile devices while using data-intensive applications by finding the optimal offloading decisions. This paper proposes a novel efficient Data Size-Aware Offloading Model (DSAOM) for data-intensive applications and to predict the appropriate resource provider for dynamic resource allocation in mobile cloud computing. Based on the data size, the tasks are separated and gradually allocated to the appropriate resource providers for execution. The task is placed into the appropriate resource provider by considering the availability services in the fog nodes or the cloud. The tasks are split into smaller portions for execution in the neighbor fog nodes. To execute the task in the remote side, the offloading decision is made by using the min-cut algorithm by considering the monetary cost of the mobile device. This proposed system achieves low-latency time 13.2% and low response time 14.1% and minimizes 24% of the energy consumption over the existing model. Finally, according to experimental findings, this framework efficiently lowers energy use and improves performance for data-intensive demanding application activities, and the task offloading strategy is effective for intensive offloading requests.