  We analyze (2+1)-dimensional Gross-Neveu model with a Thirring interaction,
where a vector-vector type four-fermi interaction is on equal terms with a
scalar-scalar type one. The Dyson-Schwinger equation for fermion self-energy
function is constructed up to next-to-leading order in 1/N expansion. We
determine the critical surface which is the boundary between a broken phase and
an unbroken one in ($\alpha_c,~ \beta_c,~ N_c$) space. It is observed that the
critical behavior is mainly controlled by Gross-Neveu coupling $\alpha_c$ and
the region of the broken phase is separated into two parts by the line
$\alpha_c=\alpha_c^*(=\frac{8}{\pi^2})$. The mass function is strongly
dependent upon the flavor number N for $\alpha > \alpha_c^*$, while weakly for
$\alpha < \alpha_c^*$. For $\alpha > \alpha_c^*$, the critical flavor number
$N_c$ increases as Thirring coupling $\beta$ decreases. By driving the CJT
effective potential, we show that the broken phase is energetically preferred
to the symmetric one. We discuss the gauge dependence of the mass function and
the ultra-violet property of the composite operators.
