Thermal stability of the electroless deposited Cu thin film was investigated. Cu/TaN/Si multilayer was fabricated by electroless-depositing Cu thin layer on TaN diffusion barrier layer which was deposited by MOCVD on the Si substrate, and was annealed in $H_2$ ambient to investigate the microstructure of Cu film with a post heat-treatment. Cu thin film with good adhesion was successfully deposited on the surface of the TaN film by electroless deposition with a proper activation treatment and solution control. Microstructural property of the electroless-deposited Cu layer was improved by a post-annealing in the reduced atmosphere of $H_2$ gas up to $600^{circ}C$. Thermal stability of Cu/TaN/Si system was maintained up to $600^{circ}C$ annealing temperature, but the intermediate compounds of Cu-Si were formed above $650^{circ}C$ because Cu element passed through the TaN layer. On the other hand, thermal stability of the Cu/TaN/Si system in Ar ambient was maintained below $550^{circ}C$ annealing temperature due to the minimal impurity of $O_2$ in Ar gas.