In our recent study, we revealed the intriguing properties of the ferromagnetic state in the Kondo lattice model with antiferromagnetic coupling in infinite dimensions: within the ferromagnetic metallic phase, the minority conduction electrons form a gap at the Fermi energy and do not participate in transport, irrespective of interaction strength and filling. This half-metallic state is referred to as a spin-selective Kondo insulator. Here we show that the spin-selective Kondo insulator can also be realized in the one-dimensional Kondo lattice model by studying static and dynamical quantities with the density-matrix renormalization group. The emergence of the spin-selective Kondo insulator, both in one and infinite dimensions, certainly demonstrates that this mechanism is quite general and ubiquitous for the ferromagnetic state in the Kondo lattice model, irrespective of the dimensionality of the system. © 2012 American Physical Society.