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.