  In the present study, we derive the problem of constructing a hypersurface
family from a given isogeodesic curve in the 4D Galilean space
$\mathbf{G}_{4}.$ We obtain the hypersurface as a linear combination of the
Frenet frame in $\mathbf{G}_{4}$ and examine the necessary and sufficient
conditions for the curve as a geodesic curve$.$ Finally, some examples related
to our method are given for the sake of clarity.
