The variation of electrical properties of (Ba, Sr)TiO$_3$[BST] thin films deposited of RuO$_2$electrode with (Ba+Sr)/Tr ration was investigated. BST thin films with various (Ba+Sr)/Tr ration were deposited on RuO$_2$/Si substrates using in-situ RF magnetron sputtering. It was found that the electrical properties of BST films depends on the composition in the film. The dielectric constant of the BST films is about 190 at the (Ba+Sr)/Tr ration of 1.0, 1,025 and does not change markedly. But , the dielectric constant degraded to 145 as the (Ba+Sr)/Tr ratio increase to 1.0. In particular, the leakage current mechanism of the films shows the strong dependence on the (Ba+Sr)/Tr ration in the films. At the ration (Ba+Sr)/Tr=1,025, the Al/BST/RuO$_2$ capacitor show the most asymmetric behavior in the leakage current density, vs, electric field plot. It is considered that the leakage current of the (Ba+Sr)/Tr=1,025 thin films is controlled by the battier-Iimited process, i,e, Schottky emission.