With the downward scaling of IC critical dimension, the speed of SiGe heterqjunction bipolar transistors has been increased dramatically. The speed of HBTs is dominated by the base transit time, which may be strongly influenced by the doping profile in the base region and the Ge concentration of base region. Therefore, the determination of the doping profile and Ge concentration of base region is crucial for design of SiGe HBTs in advanced communication circuits. In this study, the design of HBTs is transformed to a convex optimization problem, and solved efficiently by geometric programming approach. The result shows that a 23% Ge fraction may maximize the current gain and a 12.5% Ge can maximize the cut-off frequency, where 254 GHz is achieved. The accuracy of the optimization technique was confirmed by TCAD simulation. This study successfully transforms the device characteristic and manufacturing limitation into a geometric programming model and provides an insight into design of SiGe HBTs.