Flexible $BaTiO_3$ films as dielectric materials for high energy density capacitors were deposited on polyethylene terephthalate (PET) substrates by r.f. magnetron sputtering. The growth behavior, microstructure and electrical properties of the flexible $BaTiO_3$ films were dependent on the sputtering pressure during sputtering. The RMS roughness and crystallite size of the $BaTiO_3$ increased with increasing sputtering pressure. All $BaTiO_3$ films had an amorphous structure, regardless of the sputtering pressures, due to the low PET substrate temperature. The composition of films showed an atomic ratio (Ba:Ti:O) of 0.9:1.1:3. The electrical properties of the $BaTiO_3$ films were affected by the microstructure and roughness. The $BaTiO_3$ films prepared at 100 mTorr exhibited a dielectric constant of ~80 at 1 kHz and a leakage current of $10^{-8}A$ at 400 kV/cm. Also, films showed polarization of $8{mu}C/cm^2$ at 100 kV/cm and remnant polarization ($P_r$) of $2{mu}C/cm^2$. This suggests that sputter deposited flexible $BaTiO_3$ films are a promising dielectric that can be used in high energy density capacitors owing to their high dielectric constant, low leakage current and stable preparation by sputtering.