In this work, we theoretically optimize the high frequency property of silicon-germanium heterojunction bipolar transistors (HBTs) using a geometry programming (GP) technique. It is known that the base transit time of semiconductor devices potentially is a function of doping profile, device geometry and materials which significantly dominate the high frequency property of HBTs. To maximize the cut-off frequency of HBTs, the subject is formulated as a GP optimization problem by physically considering the base transit time as an object function. The GP model is solved numerically so that the cutoff frequency of HBT could be optimized for specified upper and lower bounds of the base doping concentration, and certain Ge composition. This work also shows that for 13% Ge profile, the cut-off frequency may reach a maximal value.