The phonon transport properties of CuSCN and CuSeCN have been investigated using the density functional theory and semiclassical Boltzmann transport theory. The Perdew–Burke–Ernzerhof functional shows an indirect (direct) electronic band gap of 2.18 eV (1.80 eV) for CuSCN (CuSeCN). The calculated phonon band structure shows that both compounds are dynamically stable. The Debye temperature of the acoustic phonons is 122 and 107 K for CuSCN and CuSeCN, respectively. The extended in-plane bond lengths as compared to the out-of-plane bond lengths result in phonon softening and hence, low lattice thermal conductivity. The calculated room temperature in-plane (out-of-plane) lattice thermal conductivity of CuSCN and CuSeCN is 2.39 W/mK (4.51 W/mK) and 1.70 W/mK (3.83 W/mK), respectively. The high phonon scattering rates in CuSeCN give rise to in-plane low lattice thermal conductivities. The room-temperature Grüneisen parameters of CuSCN and CuSeCN are found to be 0.98 and 1.08, respectively.