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

Delta expansion and Wilson fermion in the Gross-Neveu model: Compatibility with linear divergence and continuum limit from inverse-mass expansion