Arterial stiffness is an independent risk factor for cardiovascular diseases (CVD). Aortic pulse wave velocity (aoPWV) is a clinically used parameter for the arterial stiffness estimation, although it is influenced by blood pressure (BP). The aim of this study was to investigate whether and how aoPWV measurements obtained with a brachial single-cuff oscillometric device Arteriograph could be BP normalized. An exploratory study was conducted in 26 apparently healthy subjects (25–72 years). The aoPWV measurements were carried out in the supine position and during maneuvers designed to rise arterial BP. The aoPWV values were then normalized using mean arterial blood pressure (MAP). A moderate linear relationship (r = 0.53, p < 0.001) was observed between MAP and aoPWV with individual-specific linear models describing the relationship for each subject. It was shown that the subjects with elevated arterial BP and aoPWV had a BP normalized aoPWV (aoPWVnorm) below 10 m/s. This indicates that the cause for an increased aoPWV (>10 m/s) was the increased BP rather than the increased intrinsic stiffness of the arteries. Measurement of aoPWV at different BP levels is suggested to enable subject-specific BP normalization when estimating arterial stiffness.