A new theory for the low coherence laser amplification in rare ions doped glass has been proposed. Based on one-dimensional continuous energy level assumption and independent response assumption, the theory can describe the amplification of low coherence laser pulses with any time scale and any bandwidth. By the new theory, McCumber formula can be obtained, and a complete low coherence optical pulse amplification model in neodymium glass is established. Computation shows that at high fluences, inhomogeneous broadening will severely limit energy extraction of narrowband high coherence laser, therefore the extraction of broadband low coherence laser will exceed that of narrowband high coherence laser. In addition, the portion of long-wave of the output spectrum is slightly larger than that predicted by the homogeneous model. The new theory could be beneficial for the studies of low coherence pulse amplification in rare earth doped medium and other laser mediums.