Starting from the Maxwell equation and material density equation, the vector theory of simultaneous gain and loss stimulated Brillouin scattering (SBS) is developed for the first time. During the derivation, the effect of electrostriction on SBS is described through mathematical express. At the same time, it is found that the parameters (linewidth and Brillouin frequency) differ from each other in gain and loss spectrum theoretically. Moreover, the vector models in Jones space and Stokes space are concluded. It′s the most comprehensive vector theory of SBS as far as concerned. The theory complete the system of SBS, and will make numerous differences in the fields of SBS-based polarization effects, polarization pulling and birefringence measurement. Based on the vector theory, the effects of birefringence and polarization on average SBS gain are simulated and analyzed.