We study the ground-state properties of the double-chain Hubbard model coupled with ferromagnetic exchange interaction by using the weak-coupling theory, density-matrix renormalization-group technique, and Lanczos exact-diagonalization method. We determine the ground-state phase diagram in the parameter space of the ferromagnetic exchange interaction and band filling. We find that, in high electron-density regime, the spin gap opens and the spin-singlet
dxy-wave-like pairing correlation is most dominant, whereas in low electron-density regime, the fully-polarized ferromagnetic state is stabilized where the spin-triplet
py-wave-like pairing correlation is most dominant.