In a Dirac nodal line semimetal, the bulk conduction and valence bands touch at extended lines in the Brillouin zone. To date, most of the theoretically predicted and experimentally discovered nodal lines derive from the bulk bands of two- and three-dimensional materials. Here, based on combined angle-resolved photoemission spectroscopy measurements and first-principles calculations, we report the discovery of node-line-like surface states on the (001) surface of LaBi. These bands derive from the topological surface states of LaBi and bridge the band gap opened by spin-orbit coupling and band inversion. Our first-principles calculations reveal that these "nodal lines" have a tiny gap, which is beyond typical experimental resolution. These results may provide important information to understand the extraordinary physical properties of LaBi, such as the extremely large magnetoresistance and resistivity plateau.