The most important and challenging problem in bioinformatics is protein secondary structure prediction. The molecules of all protein organisms have three-dimensional (primary, secondary, 3-D) structures which are completely recognized by the sequence of amino acids. Protein secondary structure attributes to the polypeptide backbone of the local configuration of proteins. Most generally, the second-level prediction is indicated such as: If there is an amino acid sequence of the protein, then predict that all amino acid has in the α-Helices (H), β-sheet (E), and other Random Coils (C). In this study, Hybrid Recurrent Neural Networks (HRNN) have been proposed for the prediction of protein secondary structure to improve the prediction performance. The purpose of the work is to predict the protein secondary structure and bring out a highly accurate solution that would be easily solved in computational biology. The proposed method can experimentally perform exceedingly better than other previous work and this study could be easily understandable by researchers for solving the protein structure prediction problems. The five techniques are used for this implementation. These are Gated Recurrent Unit (GRU), Long Short-Term Memory (LSTM), Bidirectional, Bidirectional Gated Recurrent Unit (BGRU), and Bidirectional Long Short-Term Memory (BLSTM) neural networks. Especially, the proposed two-dimensional recurrent neural network (2D-RNN) framework consisted of five models: 2D-GRU_RNN, 2D-LSTM_RNN, 2D-Bi_RNN, 2D-BiGRU_RNN, and 2D-BiLSTM_RNN. In this study, firstly the 2D recurrent neural network has been generated and combined the extracted features of protein sequence with Position-Specific Scoring Matrix (PSSM). After that, the model has been trained and tested with those datasets. Finally, the model has been evaluated for prediction. Besides, all prediction accuracy has been compared and improved with existing methods. These achievements are obtained 91% (BiGRU and BiLSTM), 92% (BiGRU), 89% (BiGRU and BiLSTM), 93% (BiGRU and BiLSTM), 88% (BiGRU), 86% (BiGRU), 91% (GRU), 87% (BiLSTM), 88% (BiGRU) and 93% (GRU and BiGRU) for predicting accuracy of Q3.