We report on our calculation of the $B \to D^{(*)}\ell\nu$ form factors in 2+1 flavor lattice QCD. The Moebius domain-wall action is employed for light, strange, charm and bottom quarks. At lattice cutoffs $a^{-1} \sim 2.4$, 3.6 and 4.5 GeV, we simulate bottom quark masses up to 0.7 $a^{-1}$ to control discretization errors. The pion mass is as low as 230 MeV. We extrapolate the form factors to the continuum limit and physical quark masses, and make a comparison with recent phenomenological analyses.