We report design, modeling, analysis, and experimental study of a vibration-based piezoelectric energy harvester. The energy harvester is made of a composite cantilever of a single crystal relaxor ferroelectric material, (1- x)Pb(Mg1/3Nb2/3)O3-xPbTiO3 (PMN-PT), and a polydimethylsiloxane (PDMS) base layer. A PDMS proof mass is constructed at the tip of the composite cantilever beam and is used as a means to tune the system natural frequency. The use of the PMN-PT piezoelectric material and an interdigited electrodes (IDEs) design improves the energy conversion efficiency. A dynamic systems modeling approach is employed to analyze the responses and the performance of the harvester design. We have demonstrated that a prototype of the harvester with a size of 7.4 mm times 2 mm times 110 mum outputs a voltage of 10 V (0.3 mW power) under a vibration excitation with a peak-to-peak amplitude of 1 mm at a frequency around 1.3 kHz. Based on the experimental results, the power density prediction of the proposed harvester design shows a superior performance than that of the other reported piezoelectric harvesters.