High-performance fibers have been obtained on the basis of fusible semicrystalline R-BAPB polyimide (PI) matrix and single-wall carbon nanotubes by the melt spinning method. The resulting fibers have been subjected to orientational drawing and crystallization annealing. An effect of introducing the single-wall carbon nanotubes as well as orientation drawing and crystallization annealing on the crystallizability, structure, and mechanical properties of the composite PI fibers has been investigated. The use of the carbon nanotubes induces heterogeneous nucleation of the crystalline phase of PI on the surface of the nanoparticles. The introduction of the carbon nanoparticles increases the crystallization rate and reduces the shrinkage of the oriented fibers during annealing, making it possible to obtain crystallized PI fibers with enhanced mechanical characteristics.