  We study modular symmetric quark flavor models without fine-tuning. Mass
matrices are written in terms of modular forms, and modular forms in the
vicinity of the modular fixed points become hierarchical depending on their
residual charges. Thus modular symmetric flavor models in the vicinity of the
modular fixed points have a possibility to describe mass hierarchies without
fine-tuning. Since describing quark hierarchies without fine-tuning requires
$Z_n$ residual symmetry with $n\geq 6$, we focus on $\Gamma_6$ modular symmetry
in the vicinity of the cusp $\tau=i\infty$ where $Z_6$ residual symmetry
remains. We use only modular forms belonging to singlet representations of
$\Gamma_6$ to make our analysis simple. Consequently, viable quark flavor
models are obtained without fine-tuning.
