  In recent few years, the Gauss-Bonnet $f(\mathcal{G},\mathrm{\textit{T}})$
theory of gravity has fascinated considerable researchers owing to its coupling
of trace of the stress-energy tensor $T$ with the Gauss-Bonnet term
$\mathcal{G}$. In this context, we focuss ourselves to study bouncing universe
with in $f(\mathcal{G},\mathrm{\textit{T}})$ gravity background. Some important
preliminaries are presented along with the discussion of cosmological
parameters to develop a minimal background about
$f(\mathcal{G},\mathrm{\textit{T}})$ theory of gravity. The exact bouncing
solutions with physical analysis are provided with the choice of two equation
of state parameters. It is shown that the results do agree with the present
values of deceleration, jerk and snap parameters. Moreover, it is concluded
that the model parameters are quite important for the validity of conservation
equation (as the matter coupled theories do not obey the usual conservation
law).
