  We determine the renormalization constants for flavor non-singlet fermion
bilinear operators of M\"obius domain-wall fermions. The renormalization
condition is imposed on the correlation functions in the coordinate space, such
that the non-perturbative lattice calculation reproduces the perturbatively
calculated counterpart at short distances. The perturbative expansion is
precise as the coefficients are available up to $O(\alpha_s^4)$. We employ
$2+1$-flavor lattice ensembles at three lattice spacings in the range
0.044--0.080~fm.
