The specific strength of a carbon nanotube (CNT) fiber can be estimated to be much higher than its real value when the linear density of the fiber is measured using the vibroscopic method. This is because CNT fibers are not made of a single fiber, as assumed in the standard ASTM procedure, but rather have a hierarchical structure composed of CNTs and CNT bundles. Based on careful investigation, a new procedure using the vibroscopic method is proposed to drastically reduce the probability of erroneous results and provide a more reliable tool to investigate the mechanical properties of one-dimensional nanostructured fibers.