So far a detailed study on Heterojunction Bipolar Transistor made of Inp/InGaAs with nearly Gaussian Base doping profile , has not been done .Because of that a detailed study on Inp-InGaAs HBT is presented in this work. Two important factors for determining the performance of a transistor are base transit time and current gain (β). Variations of base transit time and gain with temperature and other device parameters for both uniform and non-uniform base doping profiles are studied here. The non-uniform base doping profile studied here is nearly Gaussian in nature. Dependence of diffusion coefficient (Dn) on temperature (T) and base doping concentration (Na) are taken into account in this study. Dependence on composition variation in the base is also taken into consideration. Also studied Gummel No in relation with base doping concentration (Na(x)). I think this work may be helpful for the final year students of Bachelor Degree and Master Degree, if they work on HBTs and their different device parameters and all those who have interest in latest works and developments in the field of Electronic Devices.