The linear stability of fiber suspensions between two concentric cylinders rotating independently is studied. The modified stability equation is obtained based on the fiber orientation model and Hinch-Leal closure approximation. The primary instabilities and bicritical curves have been calculated numerically. The critical Reynolds number,wavenumber and wave speeds of fiber suspensions as functions of the aspect ratio,volume concentration of the fibers and the gap width of cylinders are obtained. The linear stability of fiber suspensions between two concentric cylinders rotating independently is studied. The modified instability equations are obtained based on the fiber orientation model and Hinch-Leal closure approximation. The primary instabilities and bicritical curves have been calculated numerically. The critical Reynolds number, wavenumber and wave speeds of fiber suspensions as functions of the aspect ratio, volume concentration of the fibers and the gap width of cylinders are obtained.