  We obtain a class of new anisotropic relativistic solution in Einstein
Gauss-Bonnet (EGB) gravity with Finch-Skea metric in hydrostatic equilibrium.
The relativistic solutions are employed to construct anisotropic stellar models
for strange star with MIT Bag equation of state $ p_{r}= \frac{1}{3} \left(
\rho - 4 B_{g}\right)$, where $B_{g}$ is the Bag constants. Considering the
mass and radius of a known star PSR J0348+0432 we construct stellar models in
the framework of higher dimensions. We also predict the mass and radius of
stars for different model parameters. The Gauss-Bonnet coupling term ($\alpha$)
plays an important role in determining the density, pressure, anisotropy
profiles and other features. The stability of the stellar models are probed
analyzing the different energy conditions, variation of sound speed and
adiabatic stability conditions inside the star. The central density and
pressure of a star in EGB gravity are found to have higher values compared to
that one obtains in Einstein gravity ($\alpha =0$). We also explore the effect
of extra dimensions for the physical features of a compact object. For this we
consider $D=5$ and $D=6$ to obtain a realistic stellar model and found that in
the formal case both positive and negative values of $\alpha$ are allowed. But
in the later case, only $\alpha <0$ permits compact object in the Finch-Skea
metric. We determine the best fit values of the model parameters for a number
of observed stars for acceptable stellar models.
