Phase-change materials (PCMs) have received considerable attention to take advantage of both pad-type and grease-type thermal interface materials (TIMs). However, the critical drawbacks of leaking, non-recyclability, and low thermal conductivity (κ) hinder industrial applications of PCM TIMs. Here, leakage-free healable PCM TIMs with extraordinarily high κ and low total thermal resistance (Rt) are reported. The matrix material (OP) is synthesized by covalently functionalizing octadecanol PCM with polyethylene-co-methyl acrylate-co-glycidyl methacrylate polymer through the nucleophilic epoxy ring opening reaction. The OP changes from semicrystalline to amorphous above the phase-transition temperature, preventing leaking. The hydrogen-bond-forming functional groups in OP enable nearly perfect healing efficiencies in tensile strength (99.7%), κ (97.0%), and Rt (97.4%). Elaborately designed thermally conductive fillers, silver flakes and multiwalled carbon nanotubes decorated with silver nanoparticles (nAgMWNTs), are additionally introduced in the OP matrix (OP-Ag-nAgMWNT). The nAgMWNTs bridge silver-flake islands, resulting in extraordinarily high κ (43.4 W m−1 K−1) and low Rt (30.5 mm2 K W−1) compared with PCM TIMs in the literature. Excellent heat dissipation and recycling demonstration of the OP-Ag-nAgMWNT is also carried out using a computer graphic processing unit. The OP-Ag-nAgMWNT is a promising future TIM for thermal management of mechanical and electrical devices.