A new type of Pb(Mgl1/3Nb2/3)O3 (PMN) based thin film decoupling capacitor for high speed digital circuits is presented. The thin film capacitor fabricated on a ceramic Al2O3 substrate with Ball Grid Array (BGA) terminations showed low impedance and low inductance characteristics in the 100MHz – 1GHz range. The sol-gel derived Pb(Mg1/3Nb2/3)O3-PbTiO3(PMN-PT) thin film showed a high dielectric constant (k=3000) with broad temperature dependence. The capacitor consists of a PMN-PT thin film (0.8 µm thickness), Au electrodes, and solder balls mounted on the upper electrode as terminals. Numerical simulations based on the Partial Element Equivalent Circuit (PEEC) model were conducted for the design of electrodes, which gives low inductance of the capacitor. It was shown that the thin film 1.2mm × 1.2mm capacitor mounted on a board exhibits high capacitance of 20 nF, low ESR of 100 mΩ, and low inductance of 135 pH. These values are in good agreement with the results of numerical simulations.