Hybrid rockets can be an alternative to solid and liquid propellant systems, having improved safety, controllability, and high energetic performance. One of the features characterizing hybrid propulsion is a relatively low thrust due to low regression rate of the fuel. This may be a drawback for certain missions. Fuels with a higher regression rate while maintaining good mechanical properties may be of great advantage. This article investigates experimentally and theoretically a new direction to achieve this goal: the addition of expandable graphite (EG) to the fuel. EG exists as fine particles (typically, 100-400 mu m). At elevated temperatures, they expand and form strings several times longer than the original particles. When mixed with a fuel matrix they can increase the heat transfer into the fuel via conduction through the EG strings, thus increasing the regression rate. Static firing tests employing gaseous oxygen as an oxidizer and either polymeric (polyester) or liquefying (paraffin wax) fuels (plain or with 5% EG additive) have been conducted. The test results revealed an increase of 30-200% in the fuel regression rate due to EG addition, with a larger effect on the polymeric fuel and a lesser effect on the paraffin wax. Theoretical model predictions demonstrated good agreement with the experimental results.