Because stimulated Brillouin scattering is polarization related, in Brillouin optical time-domain analysis (BOTDA) sensing system, the steady measurement of sensing signals is seriously affected by the random change of polarization state of pump light and probe light, which causes the measured signal fluctuant. Through constructing coupling equations about the polarization states of pump light and probe light, we deduce the function about probe light intensity referred to the polarization state of pump light and probe light. And a novel method, called polarization expanding receiving method, is proposed to eliminate the polarization related signal fading. Numerically simulated results of coupling equations prove that the polarization expanding receiving technique is feasible for Brillouin optical time-domain analysis (BOTDA), and the theoretical analysis is correct. Finally, a primary experimental result with the proposed method is present, which is coincident with the theoretical and simulating results.