  In this paper, we investigate the spinless stationary Schr\"odinger equation
for the electron when it is permanently bound to a generalized Ellis-Bronnikov
graphene wormhole-like surface. The curvature gives rise to a geometric
potential affecting thus the electronic dynamics. The geometry of the
wormhole's shape is controlled by the parameter $n$ which assumes even values.
We discuss the role played by the parameter $n$ and the orbital angular
momentum on bound states and probability density for the electron.
