Stimulated Brillouin backscattering of an intense hollow Gaussian laser beam (HGLB) from collisionless plasma has been investigated under relativistic–ponderomotive regime. The main feature of considered hollow Gaussian laser beam is having the same power at different beam orders with null intensity at the center. Backscattered radiation is generated due to nonlinear interaction between main beam (pump beam) with pre-excited ion acoustic wave (IAW). Modified coupled equations has been set up for the beam width parameters of the main beam, ion-acoustic wave, back-scattered wave, and back reflectivity of stimulated Brillouin scattering (SBS) with the help of the Wentzel–Kramers–Brillouin approximation, fluid equations and paraxial theory approach. These coupled equations are solved analytically and numerically to study the laser intensity in the plasma, the variation of amplitude of the excited IAW and back reflectivity of SBS. The back reflectivity of SBS is found to be highly sensitive to the order of the HGLB, intensity of main laser beam, and plasma density for typical laser and plasma parameters. The focusing of main laser beam (hollow Gaussian) and IAW significantly affected the back reflectivity of SBS. The results show that the self-focusing and back reflectivity is enhanced for higher order modes of HGLB.