We investigate the single-photon transport properties in a double-waveguide quantum electrodynamic system. We force the energy degeneracy of the collective states by adjusting the direct coupling strength between the two giant atoms. Our results indicate that resonant photons can be completely transferred between the two waveguides owing to the scattering interference of eigenstates, which also results in the directional propagation of resonant photons in the output waveguide. Perfect transfer occurs when the two scattering states degenerate in the energy and decay rates. We further propose a simple scheme to realize the efficient photon transfer with directional control. This study has potential applications in quantum networks and integrated photonic circuits.