Aim: Continuous blood pressure (BP) monitoring can provide invaluable information for cardiovascular disease (CVD) diagnosis. The purpose of this study is to develop a deep recurrent neural network (RNN) model with an optimal feature set of photoplethysmogram (PPG) and electrocardiogram (ECG) signals for continuous BP estimation. Methods: This paper presents a novel deep recurrent neural network (RNN), which consists of 2-layered bidirectional Long Short-term Memory (Bi-LSTM) and 6-layered LSTM networks. It is used to estimate BP based on the optimal feature set of PPG and ECG signals. In this work, the optimal feature set is determined using five different feature selection methods. Results: The proposed method is evaluated based on 660 subjects from the University of California Irvine (UCI) machine learning repository. The RNN model with optimal feature set achieved root mean square error (RMSE) of 3.223 and 1.781 mmHg for systolic BP (SBP) and diastolic BP (DBP), respectively. It also showed mean absolute error (MAE) of 2.514 and 1.383 mmHg for SBP and DBP, respectively. Regarding the British Hypertension Society (BHS) standard, the results attained grade A for the estimation of SBP and DBP. Conclusion: The experimental results suggest that the proposed deep RNN model with an optimal feature set can improve the performance of BP prediction. Thus, it is possible to further apply our proposed method to develop a wearable device for real-time BP monitoring.