© 2017 American Physical Society. Topological insulators represent unusual topological quantum states, typically with gapped bulk band structure but gapless surface Dirac fermions protected by time-reversal symmetry. Recently, a distinct kind of topological insulator resulting from nonsymmorphic crystalline symmetry was proposed in the KHgX (X=As, Sb, Bi) compounds. Unlike regular topological crystalline insulators, the nonsymmorphic glide-reflection symmetry in KHgX guarantees the appearance of an exotic surface fermion with hourglass shape dispersion (where two pairs of branches switch their partners) residing on its (010) side surface, contrasting to the usual two-dimensional Dirac fermion form. Here, by using high-resolution angle-resolved photoemission spectroscopy, we systematically investigate the electronic structures of KHgSb on both (001) and (010) surfaces and reveal the unique in-gap surface states on the (010) surface with delicate dispersion consistent with the "hourglass Fermion" recently proposed. Our experiment strongly supports that KHgSb is a nonsymmorphic topological crystalline insulator with hourglass fermions, which serves as an important step to the discovery of unique topological quantum materials and exotic fermions protected by nonsymmorphic crystalline symmetry.