The BST $({Bal-xSrxTiO_3})$ (50/50) thin film has been grown by RF magnetron reactive sputtering and its characteristics such as crystallization, surface roughness, and electrical properties have been investigated with varying the film thickness. The crystallization and surface roughness of BST thin film are investigated by using XRD and AFM, respectively. The BST thin film annealed at $800^{circ}C$ for 2 min has pure perovskite structure and good surface roughness of 16.1$AA$. As the film thickness increases from 80 nm to 240 nm, the dielectric constant at 10 KHz increases from 199 to 265 and the leakage current density at 250 ㎸/cm decreases from $0.779 {mu}A/{cm^2} to 0.184 {mu}A/{cm^2}$. In the case of 240 nm-thick BST thin film, the charge storage density and leakage current density at 5V are 50.5 fC/${{mu}m^2} and 0.182 {mu}A/{cm^2}$, respectively. The values indicate that the BST thin film is a very useful dielectric material for the DRAM capacitor.