The constitutive equation of fiber suspensions is established on the basis of fiber orientation tensors. The modified Orr-Sommerfeld stability equation is obtained further and numerically solved by aid of spectral method and finite difference method. The computational results of channel flow without fibers agree well with the experimental data with a higher degree of accuracy than previous numerical results. The results of the channel flow with fiber suspensions indicate that the presence of fibers attenuates the instability of flow, increases the critical Reynolds number, reduces the growth rate of perturbations and narrows the range of unstable waves. The extent of the effect of fibers on the flow stability is in direct proportion to the volume fraction and aspect-ratio of the fibers.