Dielectric properties and structure of (1-x) BiFeO3 (BFO) - x Ba0.5Sr0.5TiO3 (BST) (x = 0 ∼1) solid solution thin films were investigated. All films were prepared at 600 oC on (111) oriented Pt / TiO2 / SiO2 / Si substrates by pulsed laser deposition (PLD) technique. Solid solution could be achieved in all composition ranges, evidenced by X-ray diffraction (XRD) and field emission scanning electric microscope (FE-SEM). The intermediate compositions (0.4 = x = 0.8) exhibited a distinct (111) oriented cubic perovskite structure, while rhombohedra symmetry was found in the x < 0.4 range. Dielectric constant and tunability of the (1-x) BFO – x BST films within this composition region (0.4 = x = 0.8) decreased from 1110 to 920 at 1 MHz, and increased from 28.34 % to 32.42 % at 200 kV/cm, respectively, while loss tangent remains constant. A systematic decrease in lattice parameter with BST addition reduced stress due to reduction of lattice parameter mismatch between film and the substrate. In that range, the improvement of the dielectric properties without a degradation of loss tangent is attributed to the presence of the stress relaxation, which was quantitatively confirmed by a surface profiler based on Stoney's equation.