Technological innovation has given rise to a new form of bullying, often leading to significant harm to one's reputation within social circles. When a single person becomes target to animosity and harassment in a cyberbullying incident, it is termed as denigration. Many different cyberbullying detection techniques are carried out to counter this, concentrating on word-based data and user account features only. The main objective of this research is to enhance the learning rate of long short-term memory (LSTM) using cyclic learning rate (CLR). Therefore, in this research, cyberbullying in social media is detected by developing a framework based on LSTM-CLR which is more stable for enhancing classification accuracy without the need for multiple trials and modifications. The effectiveness of the suggested LSTM-CLR is assessed for identifying cyberbullying using Twitter data. The attained results show that the proposed LSTM-CLR obtains 82% accuracy, 80% precision, 83% recall and 81% F-measure in the classification of cyberbullying tweets, which is superior when compared with the existing multilayer perceptron (MLP) and bidirectional encoder representations from transformers (BERT) models.