The possibility of effective amplification of self-similar frequency-modulated pulses in longitudinally nonuniform erbium-doped optical fibers has been studied. A general expression is obtained for the coordinate dependence of the normal dispersion of group velocities that ensures “fast” amplification of the frequency-modulated pulses. It is shown that, at an optimum choice of the dispersion profile, subpicosecond pulses can be amplified up to energies above 1 nJ and peak powers above 50 kW.