With the packing density growing continuously in integrated electronic devices, sufficient heat dissipation becomes a serious challenge. Recently, dielectric materials with high thermal conductivity have brought insight into effective dissipation of waste heat in electronic devices to prevent them from overheating and guarantee the performance stability. Layered CrOCl, an anti-ferromagnetic insulator with low-symmetry crystal structure and atomic level flatness, might be a promising solution to the thermal challenge. Herein, we have systematically studied the thermal transport of suspended few-layer CrOCl flakes by micro-Raman thermometry. The CrOCl flakes exhibit high thermal conductivities along zigzag direction, from ~ 392 ± 33 to ~ 1,017 ± 46 W·m⁻¹·K⁻¹ with flake thickness from 2 to 50 nm. Besides, pronounced thickness-dependent thermal conductivity ratio ( ${\kappa }_{\mathrm{Z}\mathrm{Z}}$/ ${\kappa }_{\mathrm{A}\mathrm{R}}$ from ~ 2.8 ± 0.24 to ~ 4.3 ± 0.25) has been observed in the CrOCl flakes, attributed to the discrepancy of phonon dispersion and phonon surface scattering. As a demonstration to the heat sink application of layered CrOCl, we then investigate the energy dissipation in graphene devices on CrOCl, SiO₂ and hexagonal boron nitride (h-BN) substrates, respectively. The graphene device temperature rise on CrOCl is only 15.4% of that on SiO₂ and 30% on h-BN upon the same electric power density, indicating the efficient heat dissipation of graphene device on CrOCl. Our study provides new insights into two-dimentional (2D) dielectric material with high thermal conductivity and strong anisotropy for the application of thermal management in electronic devices.