Recently, thin film capacitors of high dielectric constant and low leakage current are applied to integrated devices. In this study, (Ba, Sr)$TiO_3$ (BST) thin films for low cost were prepared by Sol-Gel method. BST solution was spin-coated on Pt/$SiO_2$/Si substrate at 4,000 rpm for 10 seconds. Coating process was repeated 3 times and then sintered at $700^{circ}C$ for 30 minutes. Structural and electrical characteristics of each specimen were analyzed by TG-DTA, SEM, fractal phenomenon, voltage-current and dielectric factor. Thickness of BST ceramics thin films are about 2,600~2,800 ${AA}$ at depositing 3 times. Dielectric constant of thin films was decreased in 1 kHz~1 MHz. Dielectric constant and loss to frequency were 250 and 0.02 in $(Ba_{0.7}Sr_{0.3})TiO_3$ (BST3). Leakage current of BST3 was $10^{-9}sim10^{-11}$/ A under 3 V.