  Single crystals of NbGe$_{2}$ which crystallize in a noncentrosymmetric
hexagonal structure with chirality are synthesized and their superconductivity
is investigated. Type-I superconductivity is confirmed by dc magnetization,
field-induced second-to first-order phase transition in specific heat, and a
small Ginzburg-Landau parameter $\kappa_{GL}=0.12$. The isothermal
magnetization measurements show that there is a crossover from type-I to
type-II/1 superconductivity with decreasing temperature and an unusually
enhanced surface superconducting critical field ($H_{c3}$) is discovered. The
band structure calculations indicate the presence of Kramer-Weyl nodes near the
Fermi level. These observations demonstrate that NbGe$_{2}$ is an interesting
and rare example involving the possible interplay of type-I superconductivity,
noncentrosymmetric structure and topological properties.
