Here, two compounds, AZnSb (A = Rb, Cs), have been predicted to be potential materials for thermoelectric device applications at high temperatures by using first-principles calculations based on density functional theory (DFT), density functional perturbation theory (DFPT), and Boltzmann transport theory. The layered structure, and presence of heavier elements Rb/Cs and Sb induce high anharmonicity (larger values of mode Gruneisen parameter), low Debye temperature, and intense phonon scattering. Thus, these compounds possess intrinsically low lattice thermal conductivity (kappa(l)), similar to 0.5 W m(-1) K-1 on average at 900 K. Highly non-parabolic bands and relatively wide bandgap (similar to 1.37 and 1.1 eV for RbZnSb and CsZnSb, respectively, by mBJ potential including spin-orbit coupling effect) induce large Seebeck coefficient while highly dispersive and two-fold degenerate bands induce high electrical conductivity. Large power factor and low values of kappa(l) lead to a high average thermoelectric figure of merit (ZT) of RbZnSb and CsZnSb, reaching 1.22 and 1.1 and 0.87 and 1.14 at 900 K for p-and n-type carriers, respectively.