Cloud is a recent technology that enables wide access and storage on the internet. Moreover, the cloud computing environment allows storing and sharing plenty of digital data including text, image, video, audio, etc. through the internet. Although it is cost-effective and has numerous advantages, cloud technology still faces a lot of challenges like data loss, quality issues, and data security. In this paper, an effective algorithm is introduced using deoxyribonucleic acid (DNA)-based cryptography to enhance data security while sharing the data over the internet. For this process, an optimized encryption model is implemented using Grey Wolf Optimization (GWO) Algorithm to generate optimal encrypted data while sharing. Various datasets have been implemented to verify the efficiency of the proposed GWO Assisted-DNA (GWOA-DNA) cryptography in terms of accuracy and execution time.