A new computation method of a back-propagation neural network (BPNNs) is designed and expected to implement continuous measurement of blood pressures (BPs) by a noninvasive, cuffless, handheld strain-type BP sensor. The sensor is successfully designed to acquire pulsation signals at the wrist artery of a subject with a readout designed of a Wheatstone bridge, amplifier, filter, and a digital signal processor. To predict BP based on the obtained pulsation signals, 22 features are extracted to compute systolic blood pressure (SBP) and diastolic blood pressure (DBP) based an established BPNN. There are 22 input neurons, 30 hidden layers and 2 output neurons in BPNN model. The inputs are presented to the pulsation signal of time domain and frequency domain and outputs are presented to SBP and DBP. Experiments are conducted to show the validness of the developed sensor and BPNN. The data show that the prediction errors are within mmHg, respectively. SBP and DBP are 1.35 ± 3.45 and 2.29 ± 3.28 mmHg, respectively. The errors of blood pressure pass the criteria for Association for the Advancement of Medical Instrumentation (AAMI) method 2 and the British Hypertension Society (BHS) Grade B.