(Ba, Sr) TiO$_3$(BST) thin films were prepared on RuO$_2$/Si substrates by rf magnetron sputtering and annealing was followed at temperatures ranging from 550 to 80$0^{circ}C$ in $N_2$or $O_2$atmosphere. The effects of annealing conditions on the properties of BST film deposited on RuO$_2$bottom electrodes were investigated. It was found that the crystallinity. surface roughness, and grain size of BST films vary with the annealing temperature but they are not dependent upon the annealing atmosphere. The flat region in the current-voltage (I-V) curves of BST capacitors shortened with increasing annealing temperature under both atmospheres. This is believed to be due to the lowering of potential barrier caused by unstable interface and the increase of charge The shortening of the flat region by $O_2$annealing was more severe than that by $N_2$-annealing. As a result, there was no flat region when the films were annealed at 700 and 80$0^{circ}C$ in $O_2$atmosphere. The dielectric properties of BST films were improved by annealing in either atmosphere. however, a degradation with frequency was observed when the films were annealed at relatively high temperature under $O_2$atmosphere.