An online social media platform such as Instagram has become a popular communication channel that millions of people are using today. However, this media also becomes an avenue where fake accounts are used to inflate the number of followers on a targeted account. Fake accounts tend to alter the concepts of popularity and influence on the Instagram media platform and significantly impact the economy, politics, and society, which is considered cybercrime. This paper proposes a framework to classify fake and real accounts on Instagram based on a deep learning approach called the Long Short-Term Memory (LSTM) network. Experiments and comparisons with existing machine and deep learning frameworks demonstrate considerable improvement in the proposed framework. It achieved a detection accuracy of 97.42% and 94.21% on two publicly available Instagram datasets, with F-measure scores of 92.17% and 89.55%, respectively. Further experiments on the Twitter dataset reveal the effectiveness of the proposed framework by achieving an impressive accuracy rate of 99.42%.