Annealing of $Cu(B)/Ti/SiO_2$ in vacuum has been carried out to investigate the effects of Ti underlayer on microstructure in $Cu(B)/Ti/SiO_2$ structures. For comparison, $Cu(B)/Ti/SiO_2$ structures was also annealed in vacuum. Three different temperature dependence of Cu growth can be seen in $Cu(B)/Ti/SiO_2$; B precipitates- pinned grain growth, abnormal grain growth, normal grain growth. The Ti underlayer having a strong affinity for B atoms reacts with the out-diffused B to the Ti surface and forms titanium boride at the Cu-Ti interface. The formation of titanium boride acts as a sink for the out-diffusion of B atoms. The depletion of boron in grain boundaries of Cu films, as results of the rapid diffusion of B along the grain boundaries and the insufficient segregation of B to the grain boundaries, induces grain boundaries to migrate and causes the abnormal grain growth. The increased bulk diffusion coefficient of B within Cu grains can be responsible for the normal grain growth occurring in the annealed $Cu(B)/Ti/SiO_2;at;600^{circ}C$. In contrast, the $Cu/SiO_2$ structures show only the abnormal growth of grains and their sizes increasing as the temperature increases above $400^{circ}C$.