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In this paper, we study stability of the Einstein static universe against inhomogeneous scalar perturbations parameterized by equation of state parameter in $f(\mathcal{G},T)$ gravity ( $\mathcal{G}$ and $T$ represent the Gauss-Bonnet invariant and trace of energy-momentum tensor, respectively). We formulate static as well as perturbed field equations in the presence of perfect fluid and analyze the stability regions. This is accomplished for particular $f(\mathcal{G},T)$ models corresponding to zero as well as non-zero covariant divergence of the energy-momentum tensor. It is found that stable Einstein universe exists both for spatially closed as well as open universe models for suitable choice of parameters.