We have theoretically investigated the thermoelectric properties of impurity-doped one-dimensional semiconductors, focusing on nitrogen-substituted (N-substituted) carbon nanotubes (CNTs), using the Kubo formula combined with a self-consistent t-matrix approximation. N-substituted CNTs exhibit extremely high thermoelectric power factor (PF) values originating from a characteristic of one-dimensional materials where decrease in the carrier density increase both the electrical conductivity and the Seebeck coefficient in the low-N regime. The chemical potential dependence of the PF values of semiconducting CNTs has also been studied as a field-effect transistor and it turns out that the PF values show a noticeable maximum in the vicinity of the band edges. This result demonstrates that “band-edge engineering” will be crucial for solid development of high-performance thermoelectric materials.