Nanocomposite fibers consisting of isotactic polypropylene (iPP) as a matrix filled with vapor grown carbon nanofibers (VGCF) have been prepared and their fine crystalline structure and mechanical properties characterized. The obtained results point out that the VGCF oriented along the fiber extrusion direction induce crystallization in the surrounding iPP matrix in a special way leading to the formation of oriented iPP a-transcrystallite layers. The VGCF content and the draw ratio (DR) affect the textural properties of the composite material and lead to the formation of an anisotropic structure. The improvements of the mechanical properties of the composite fibers in both undrawn and drawn states are attributed to the VGCF aligning effect during extrusion, which produces highly oriented iPP crystalline structure, rather than to the reinforcing effect of the nanofibers. A new detailed scheme explaining the changes in tensile strength from the structural point of view is proposed.