  We propose the notion of normalized Laplacian matrix $\mathcal{L}(\Phi)$ for
a gain graphs and study its properties in detail, providing insights and
counterexamples along the way. We establish bounds for the eigenvalues of
$\mathcal{L}(\Phi)$ and characterize the classes of graphs for which equality
holds. The relationships between the balancedness, bipartiteness, and their
connection to the spectrum of $\mathcal{L}(\Phi)$ are also studied. Besides, we
extend the edge version of eigenvalue interlacing for the gain graphs.
Thereupon, we determine the coefficients for the characteristic polynomial of
$\mathcal{L}(\Phi)$.
