Drag reduction features in the transition regime of channel flow with fibre suspension were analyzed in terms of the linear stability theory. The modified stability equation was obtained based on the slender-body theory and natural closure approximation. Results of the stability analysis show attenuating effects of fibre additives to the flow instability. For the cases leading to transition, drag reduction rate increases with the characteristic parameter H of fibres. The mechanism of drag reduction by fibres is revealed through the variation of velocity profile and the decrease of wall shear stress. The theoretical results are qualitatively consistent with some typical experiments.