An alkoxide-based sol-gel method was used to fabricate $Ba_{0.6}Sr_{0.4}TiO_{3}$thin films doped by Bi from 5 to 20 mol% on a Pt/Ti/$SiO_2$/Sisubstrate. The structural and dielectric properties of BST thin films were investigated as a function of Bi dopant concentration. The dielectric properties of the Bi doped BST films were strongly dependent on the Bi contents. The dielectric constant and dielectric loss of the films decreased with increasing Bi content. However, the leakage current density of the 10 mol% Bi doped $Ba_{0.6}Sr_{0.4}TiO_{3}$ thin film showed the lowest value of 5.13$ imes 10^{-7} A/{cm}^2$ at 5 V. The figure of merit (FOM) reached a maximum value of 32.42 at a 10 mol% Bi doped $Ba_{0.6}Sr_{0.4}TiO_{3}$thin films. The dielectric constant, loss factor, and tunability of the 10 mol% Bi doped $Ba_{0.6}Sr_{0.4}Tio_{3}$ thin films were 333, 0.0095, and 31.1%, respectively.