A linear stability analysis on the circular pipe flow of fiber suspensions is presented. The fiber orientation tensors are used to describe the characteristics of the orientation distribution of fibers. The constitutive equation for the fiber suspensions is set up and the modified Orr-Sommerfeld stability equation is derived. An improved finite difference method with high order accuracy is employed to solve the equation. The Newtonian pipe Poiseuille flow corresponding to H=0 is also analyzed for comparison. The results reveal that the fiber additives will enhance the flow stability, the degree of enhancement becomes high with the increases of the parameter H which accounts for the fiber resistance to the stretching along its axis. Fiber suspensions with large H can suppress the influence of high Reynolds number on the flow stability. Particularly, fibers give a higher attenuation of the short waves of disturbance.