Flow energy harvesters (FEHs) have recently emerged as a major player in the field of micro-power generation. Such devices are designed to harness energy from a dynamic flow field, typically wind, in order to power remote, sub-milliwatt consumption sensors that are hard to access or maintain. Previous research efforts have focused on harnessing flow energy under nearly steady conditions where measurable variations in the flow speed occur at a much longer time scale than the time constant of the harvester itself. Under such conditions, the nature of the harvester's transient response is irrelevant and does not constitute a critical performance criterion. However, since gusts of wind also contain a significant amount of energy, designing FEHs to have a fast transient response is essential to capture the maximum possible energy from the flow. To address this critical issue, we propose a galloping piezoelectric energy harvester consisting of piezoelectric cantilever beam with a modified bluff body mounted at its tip. Square, trapezoid, and triangle bluff bodies were tested, each augmented with a tail fin to enhance the transient response of the harvester. It is shown experimentally that the settling time of the response and the steady state output power can be improved substantially when the fin is added.