High blood pressure is a major public health issue. However, there are many physical and non-physical factors that affect the measurement of blood pressure (BP) over very short time spans. Therefore, it is very difficult to write a mathematical equation which includes all relevant factors needed to estimate accurate BP values. As a result, a possible solution to overcome these limitations is the use of an artificial neural network (ANN). The aim of this research is to design and implement a new ANN approach, which correlates the arterial pulse waveform shape to BP values, for estimation of BP in a single heartbeat. To test the feasibility of this approach, a pilot study was performed on an arterial pulse waveform dataset obtained from 11 patients with normal BP and 11 patients with hypertension. It was found that the proposed method can accurately estimate BP in single heartbeats and satisfy the requirements of the ANSI/AAMI standard for non-invasive measurement of BP.