This paper describes the submission of the team Amrita_CEN_NLP to the shared task on Offensive Language Identification in Dravidian Languages at EACL 2021. We implemented three deep neural network architectures such as a hybrid network with a Convolutional layer, a Bidirectional Long Short-Term Memory network (Bi-LSTM) layer and a hidden layer, a network containing a Bi-LSTM and another with a Bidirectional Recurrent Neural Network (Bi-RNN). In addition to that, we incorporated a cost-sensitive learning approach to deal with the problem of class imbalance in the training data. Among the three models, the hybrid network exhibited better training performance, and we submitted the predictions based on the same.