This paper studies buckling behavior of non-uniform fiber columns under axially distributed compressive load and presents a new approach for determining buckling load. For free-built-in fibers, a Fredholm equation is derived from solving the governing equation with end constraints. Critical load and critical length can be evaluated by seeking the lowest eigen-value of the resulting equation. For the cases of the cross-sectional moment of inertia and axially distributed load as power functions with respect to the axial distance from the free end, a necessary condition for buckling is derived, and a polynomial characteristic equation is then obtained and solved. The effect of the weight and axial profile of tapered fibers on the critical length is discussed.