Nonlinear Brillouin backward scattering of a linearly polarized short laser pulse propagating through a homogenous nonextensive distributed plasma in the presence of a uniform magnetic field perpendicular to both the direction of propagation and electric vector of the radiation field is investigated theoretically when ponderomotive relativistic and nonlinearity effects up to third order are taken into account. The governing equations for nonlinear wave in the context of nonextensive statistics are given, and the nonextensive coupled equations describing the nonlinear Brillouin backward scattering instability are solved by the Fourier transformation method, and the growth rate of the nonlinear Brillouin backward scattering instability is obtained. The results in the case q→1 are consistent with those in the framework of the Maxwellian distribution. It is found that the instability growth rate increases on increasing plasma density, radiation field amplitude, and nonextensive parameter, while the instability growth rate shows a decrease due to the presence of external magnetic field.