The BST (Ba$_{1-x}$ Sr$_{x}$TiO$_{3}$)(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 anealed at 800.deg. C for 2 min has pure perovskite structure and good surface roughness of 16.1.angs.. We estimate that the thickness and dielectric constant of interface layer between BST film and electrode are 3nm and 18.9, respectively, by measuring the capacitance with various film thickness. As the film thickness increases form 80nm to 240nm, the dielectric constant at 10kHz increases from 199 to 265 and the leakage current density at 200kV/cm decreases from 0.682.mu.A/cm$^{2}$ to 0.181 .mu.A/cm$^{2}$. In the case of 240nm-thick BST thin film, the charge storage density and leakage current density at 5V are 50.5fC/.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.or.