The Kondo insulator SmB6 has long been known to exhibit low temperature (T < 10K) transport anomaly and has recently attracted attention as a new topological insulator candidate. By combining low-temperature and high energy-momentum resolution of the laser-based ARPES technique, for the first time, we probe the surface electronic structure of the anomalous conductivity regime. We observe that the bulk bands exhibit a Kondo gap of 14 meV and identify in-gap low-lying states within a 4 meV window of the Fermi level on the (001)-surface of this material. The low-lying states are found to form electron-like Fermi surface pockets that enclose the X and the Gamma points of the surface Brillouin zone. These states disappear as temperature is raised above 15K in correspondence with the complete disappearance of the 2D conductivity channels in SmB6. While the topological nature of the in-gap metallic states cannot be ascertained without spin (spin-texture) measurements our bulk and surface measurements carried out in the transport-anomaly-temperature regime (T < 10K) are consistent with the first-principle predicted Fermi surface behavior of a topological Kondo insulator phase in this material.