Thermoelectric power, S(T) of the Mg1-xAlxB2 system has been measured for x = 0.0, 0.1, 0.2, 0.4, 0.6, 0.8 and 1.0. XRD, resistivity and magnetization measurements are also presented. It has been found that the thermoelectric power is positive for x = 0.4 and is negative for x = 0.6 over the entire temperature range studied up to 300 K. The thermoelectric power of x = 0.4 samples vanishes discontinuously below a certain temperature, implying existence of superconductivity. In general, the magnitude of the thermoelectric power increases with temperature up to a certain temperature, and then it starts to decrease towards zero base line. In order to explain the observed behavior of the thermoelectric power, we have used a model in which both diffusion and phonon drag processes are combined by using a phenomenological interpolation between the low and high temperature behaviors of the thermoelectric power. The considered model provides an excellent fit to the observed data. It is further found that Al doping enhances the Debye temperature.