We present a first-principles study of the phonon transport properties of the Half-Heusler NbCoSb compound. The single crystal elastic constants have been calculated using the stress-strain method. The mechanical properties such as bulk modulus, shear modulus, Young's modulus, Poisson's ratio, and anisotropy factor are estimated using the Voigt-Reuss-Hill approximation. The Grüneisen parameters, phonon life time, and lattice thermal conductivity have been studied in detail. The elastic and phonon properties reveal that this compound is mechanically and dynamically stable. An analysis of the harmonic and anharmonic phonon dispersion and vibrational density of states reveal that, NbCoSb has a very low lattice thermal conductivity, hence, it is a candidate thermoelectric material.