  We study the large mass hierarchy and CP violation in the modular symmetric
quark flavor models without fine-tuning. Mass matrices are written in terms of
modular forms. Modular forms near the modular fixed points are approximately
given by $\varepsilon^p$, where $\varepsilon$ and $p$ denote the small
deviation from the fixed points and their residual charges. Thus mass matrices
have the hierarchical structures depending on the residual charges, and have a
possibility describing the large mass hierarchy without fine-tuning. Similar
structures of mass matrices are also obtained in Froggatt-Nielsen models.
Nevertheless, it seems to be difficult to induce a sufficient amount of CP
violation by a single small complex parameter $\varepsilon$. To realize the
large mass hierarchy as well as sizable CP violation, multi-moduli are
required. We show the mass matrix structures with multi-moduli which are
consistent with quark flavor observables including CP phase. We also discuss
the origins of the large mass hierarchy and CP violation in such mass matrix
structures.
