  We apply the $\delta$-expansion to the Gross-Neveu model in the large $N$
limit with Wilson fermion and investigate dynamical mass generation from
inverse-mass expansion. The dimensionless mass $M$ defined via the effective
potential is employed as the expansion parameter of the bare coupling constant
$\beta$ which is partially renormalized by the subtraction of linear
divergence. We show that $\delta$-expansion of the $1/M$ series of $\beta$ is
compatible with the mass renormalization. After the confirmation of the
continuum scaling of the bare coupling without fermion doubling, we attempt to
estimate dynamical mass in the continuum limit and obtain the results
converging to the exact value for values of Wilson parameter $r\in (0.8,1.0)$.
