The density-matrix renormalization group method is used to study the three-band zigzag ladder model that simulates the electronic state of the t 2g-orbital system of the double string of the edge-shared CrO 6 octahedra in the half-metallic ferromagnet K2Cr 8O16. The saturated ferromagnetism caused by the double-exchange mechanism is thereby demonstrated. We also use the Lanczos exact-diagonalization technique on small clusters to study the two Hubbard chains coupled with the ferromagnetic exchange interaction, whereby we consider the nonquasiparticle states in the half-metallic ferromagnet that appear in the single-particle spectral function.