Arterial stiffness has been proved to be an important parameter in the evaluation of cardiovascular diseases, and Pulse Wave Velocity (PWV) is a strong indicator of arterial stiffness. Compared to regional PWV (PWV among different arteries), local PWV (PWV within a single artery) outstands in providing higher precision in indicating arterial properties, as regional PWVs are highly affected by multiple parameters, e.g., variations in blood vessel lengths due to individual differences, and multiple reflection effects on the pulse waveform. However, local PWV is less-developed due to its high dependency on the temporal resolution in synchronized signals with usually low signal-to-noise ratios. This paper presents a method for the noninvasive simultaneous measurement of two local PWVs in both left and right radial arteries based on the Fiber Bragg Grating (FBG) technique via correlation analysis of the pulse pairs at the fossa cubitalis and at the wrist. Based on the measurements of five male volunteers at the ages of 19 to 21 years old, the average left radial PWV ranged from 9.44 m/s to 12.35 m/s and the average right radial PWV ranged from 11.50 m/s to 14.83 m/s. What is worth mentioning is that a stable difference between the left and right radial PWVs was observed for each volunteer, ranging from 2.27 m/s to 3.04 m/s. This method enables the dynamic analysis of local PWVs and analysis of their features among different arteries, which will benefit the diagnosis of early-stage arterial stiffening and may bring more insights into the diagnosis of cardiovascular diseases.