Abstract We investigate the behaviour of backward stimulated Raman scattering (BSRS) in inhomogeneous plasma with a transverse external magnetic field via 1D and 2D particle-in-cell simulations and theoretical analysis. The external magnetic field B e x t causes nonlinear damping of large-amplitude electron plasma waves (EPWs), and significantly limits the reflectivity of stimulated Raman scattering (SRS) even if B e x t is very weak. For a single resonance point, B e x t limits the kinetic nonlinear frequency shift, impedes the autoresonance behaviour of SRS, and narrows the resonance region. We also exhibit B e x t distorts the distribution function of electrons evidently, and alters the wavefronts of EPWs in high dimensional cases. The simulation results indicate a moderate B e x t can significantly reduce the trapped electron induced gain of SRS reflectivity, and make the BSRS reflectivity stay at its linear convective saturation level steadily.