Recently, there have been increasingly hot debates on whether a bulk Fermi surface of charge-neutral excitations exists in the topological Kondo insulator SmB_{6}. To unambiguously resolve this issue, we perform the low-temperature thermal conductivity measurements of a high-quality SmB_{6} single crystal down to 0.1 K and up to 14.5 T. Our experiments show that the residual linear term of thermal conductivity at the zero field is zero, within the experimental accuracy. Furthermore, the thermal conductivity is insensitive to the magnetic field up to 14.5 T. These results demonstrate the absence of fermionic charge-neutral excitations in bulk SmB_{6}, such as scalar Majorana fermions or spinons and, thus, exclude the existence of a bulk Fermi surface suggested by a recent quantum oscillation study of SmB_{6}. This puts a strong constraint on the explanation of the quantum oscillations observed in SmB_{6}.