  The shallow decay phase and flares in the afterglows of gamma-ray bursts
(GRBs) is widely believed to be associated with the later activation of central
engine. Some models of energy injection involve with a continuous energy flow
since the GRB trigger time, such as the magnetic dipole radiation from a
magnetar. However, in the scenario involving with a black hole accretion
system, the energy flow from the fall-back accretion may be delayed for a
fall-back time $\sim t_{\rm fb}$. Thus we propose a delayed energy injection
model, the delayed energy would cause a notable rise to the Lorentz factor of
the external shock, which will "generate" a bump in the multiple band
afterglows. If the delayed time is very short, our model degenerates to the
previous models. Our model can well explain the significant re-brightening in
the optical and infrared light curves of GRB 081029 and GRB 100621A. A
considerable fall-back mass is needed to provide the later energy, this
indicates GRBs accompanied with fall-back material may be associated with a low
energy supernova so that fraction of the envelope can be survived during
eruption. The fall-back time can give meaningful information of the properties
of GRB progenitor stars.
