In the present paper we report theoretical calculations for the Hugoniot of shock-compressed rubidium. We use an all-electron full-potential method based on density-functional theory to obtain the total energy, pressure and electronic density of states. Thermal contributions to the equation of state (EOS) were introduced through temperature dependent occupation of the electronic states and a Grüneisen model was used for determining the nuclear thermal motion. The calculated Hugoniot is in very good agreement with the shock experiments. A temperature of about 10 000 K is reached at the pressure of about 300 kbar, the highest reached experimentally. Rubidium was chosen for this study because it undergoes a sequence of unusual pressure-induced structural transitions which have been attributed to s-d electron transfer. Since most studies of s-d transfer have been carried out at temperatures below 500 K, little is known of how it effects the equation of state at very high temperature. We found that the predicted Rb Hugoniot is very sensitive to the thermal s-d electron transfer, which leads to a considerable lowering of the predicted Hugoniot pressure and temperature.