Electrocardiography (ECG) is the gold standard for monitoring vital signs and for diagnosing, controlling, and preventing cardiovascular diseases (CVDs). However, ECG requires continuous user participation, and cannot be used for continuous cardiac monitoring. In contrast to ECG, photoplethysmography (PPG) devices do not require continued user involvement, and can offer ongoing and long-term detection capabilities. However, from a medical perspective, ECG can provide more information about the heart. Currently, most existing work contains different signals recorded from the same subject in training and test sets. This study proposes a neural network model based on a 1D convolutional neural network (CNN) and a bidirectional long short-term memory (BiLSTM) network. This neural network model can directly reconstruct ECG signals from PPG signals. The learned features are captured from the CNN model and fed into the BiLSTM model. In order to verify the validity of the model, it is evaluated using the MIMIC II dataset in the completely subject-independent model (records are placed in a training set, and a test set appears once, but the test signal belongs to a record that is not in the training set). The Pearson’s correlation coefficient between the reconstructed ECG and the reference ECG of the proposed model is 0.963 in the completely subject-independence model. The results of the proposed model are better than those of several cited state-of-the-art models. The results of our trained model indicate that we can obtain reconstructed ECGs that are highly similar to reference ECGs in the completely subject-independent model.