The photoplethysmography (PPG) method for continuous noninvasive measurements of blood pressure (BP) offers a more comfortable solution than conventional methods. The main challenge in using the PPG method is that its accuracy is greatly influenced by motion artifacts. In addition, the characteristics of PPG vary depending on physiological conditions; hence, the system must be calibrated to adjust for such changes. We attempt to address these limitations and propose a novel method for the classification of BP using a bidirectional long short-term memory (BLSTM) network with time-frequency (TF) analysis based on PPG signals. The TF analysis extracts information from PPG signals using a short-time Fourier transform (STFT) in the time domain to produce two features, namely, the instantaneous frequency and spectral entropy. Training the BLSTM network using TF features significantly improves the classification performance and decreases the training time. We classify 900 PPG waveform segment samples from 219 adult subjects into three classification levels: normotension (NT), prehypertension (PHT) and hypertension (HT). The results show that the proposed method is successful in the classification of BP with accuracy, sensitivity, and speciticity values of 97.33%, 100%, and 94.87%, respectively. The F1 scores of three BP classifications were 97.29%, 97.39%, and 93.93%, respectively. A comparison of current and previous approaches to the classification of BP is accomplished. Our proposed method achieves a higher accuracy than convolutional neural networks (CNNs), k-nearest neighbors (KNN), bagged tree, logistic regression, and AdaBoost tree methods.