Three-dimensional (3D) topological insulators (TIs) are new forms of quantum matter that are characterized by their insulating bulk state and exotic metallic surface state, which hosts helical Dirac fermions1-2. Very recently, BiTeCl, one of the polar semiconductors, has been discovered by angle-resolved photoemission spectroscopy to be the first strong inversion asymmetric topological insulator (SIATI). In contrast to the previously discovered 3D TIs with inversion symmetry, the SIATI are expected to exhibit novel topological phenomena, including crystalline-surface-dependent topological surface states, intrinsic topological p-n junctions, and pyroelectric and topological magneto-electric effects3. Here, we report the first transport evidence for the robust topological surface state in the SIATI BiTeCl via observation of Shubnikov-de Haas (SdH) oscillations, which exhibit the 2D nature of the Fermi surface and pi Berry phase. The n = 1 Landau quantization of the topological surface state is observed at B . 12 T without gating, and the Fermi level is only 58.8 meV above the Dirac point, which gives rise to small effective mass, 0.055me, and quite large mobility, 4490 cm2s-1. Our findings will pave the way for future transport exploration of other new topological phenomena and potential applications for strong inversion asymmetric topological insulators.