We have investigated the effect of silver added to Cu films on the microstructure evolution, resistivity, surface morphology, stress relaxation temperature, and adhesion properties of Cu(Ag) alloy thin films deposited on Mo glue layer upon annealing. In addition, pure Cu films deposited on Mo has been annealed and compared. The results show that the silver in Cu(Ag) thin films control the grain growth through the coarsening of its precipitates upon annealing at $300^{circ}C{sim}600^{circ}C$ and the grain growth of Cu reveals the activation energy of 0.22 eV, approximately one third of activation energy for diffusion of Ag dopant along the grain boundaries in Cu matrix (0.75 eV). This indicates that the grain growth can be controlled by Ag diffusion along the grain boundaries. In addition, the grain growth can be a major contributor to the decreased resistivity of Cu(Ag) alloy thin films at the temperature of $300^{circ}C{sim}500^{circ}C$, and decreases the resistivity of Cu(Ag) thin films to $1.96{mu}{Omega}-cm$ after annealing at $600^{circ}C$. Furthermore, the addition of Ag increases the stress relaxation temperature of Cu(Ag) thin films, and thus leading to the enhanced resistance to the void formation, which starts at $300^{circ}C$ in the pure Cu thin films. Moreover, Cu(Ag) thin films shows the increased adhesion properties, possibly resulting from the Ag segregating to the interface. Consequently, the Cu(Ag) thin films can be used as a metallization of advanced TFT-LCDs.