  In this work we analyze the ground-state properties of the $s=1/2$
one-dimensional ANNNI model in a transverse field using the quantum fidelity
approach. We numerically determined the fidelity susceptibility as a function
of the transverse field $B_x$ and the strength of the next-nearest-neighbor
interaction $J_2$, for systems of up to 24 spins. We also examine the
ground-state vector with respect to the spatial ordering of the spins. The
ground-state phase diagram shows ferromagnetic, paramagnetic, floating,
$\Braket{2,2}$ phases, and we predict an infinite number of modulated phases in
the thermodynamic limit ($L \rightarrow \infty$). The transition lines
separating the modulated phases seem to be of second-order, whereas the line
between the floating and the $\Braket{2,2}$ phases is possibly of first-order.
