Epitaxial Ba1−xSrxTiO3 (BST) thin films with different Ba∕Sr ratio (x=0.1–0.9 with an interval of 0.1) have been grown on (001) LaAlO3 substrates using polymer-assisted deposition. Dielectric measurements show that the films have dielectric properties comparable to the BST films grown by the pulsed laser deposition. Systematic changes in the lattice parameters and dielectric behavior with x values have been measured. The highest dielectric constant (∼1010) and tunability (∼69%) at 1 MHz and room temperature have been obtained at x=0.3, which is at the phase boundary of tetragonal and cubic structures.