Blood pressure is an important vital sign that sometimes requires continuous measurement. The current methods include cuff measurements (manual auscultation and oscillometric techniques) for non-continuous measurement and invasive arterial cannulation for continuous measurement. The use of photoplethysmography as a cuffless, non-invasive, and continuous blood pressure measurement system is investigated through the use of four neural networks. These predict the systolic blood pressure, diastolic blood pressure, mean arterial blood pressure, and waveform shape. The models are trained on 890 h of data from 1669 patients in the MIMIC-III database. Feature-trained artificial neural networks predict the systolic blood pressure to 5.26 ± 6.53 mmHg (mean error ± standard deviation), the diastolic blood pressure to 2.96 ± 3.31 mmHg, and the mean arterial pressure to 3.27 ± 3.55 mmHg. These are used to shift and scale the predicted waveform, allowing the waveform prediction neural network to optimise for the wave shape rather than the amplitude. The waveform prediction has 86.4% correlation with the actual arterial blood pressure waveform. All results meet international clinical blood pressure measurement standards and could potentially change how blood pressure is measured in both clinical and research settings. However, more data from healthy individuals and analysis of the models’ biases based on clinical features is required.