Using nonequilibrium molecular dynamics simulations, we study the thermal conductivity of asymmetric double chains. We couple two different single chains through interchain coupling to build three kinds of asymmetric double- stranded chain system: intrachain interaction, external potential, and mass asymmetric double chains. It is reported that asymmetry is helpful in improving the thermal conductivity of the system. We first propose double-heat flux channels to explain the influence of asymmetric structures on the thermal conductivity. The phonon spectral behaviour and finite size effect are also included.