A graded-core single-polarisation fibre is proposed, and the dispersion equation for its modes is obtained. Very simple asymptotic formulas are derived giving the cutoff frequency as a function of K which determines the depth of the depressions of the cladding when K is small. By incorporating stress anisotropy, it is found that the absolute single-polarisation frequency bandwidth can be increased in the graded-core, stress-applied polarisation-maintaining fibres compared with the conventional step-index profile. The relative frequency bandwidth is approximately the same for the graded-core or step-index profiles.