  Recently, the first association between an ultra-long gamma-ray burst (GRB)
and a supernova is reported, i.e., GRB 111209A/SN 2011kl, which enables us to
investigate the physics of central engines or even progenitors for ultra-long
GRBs. In this paper, we inspect the broad-band data of GRB 111209A/SN 2011kl.
The late-time X-ray lightcurve exhibits a GRB 121027A-like fall-back bump,
suggesting a black hole central engine. We thus propose a collapsar model with
fall-back accretion for GRB 111209A/SN 2011kl. The required model parameters,
such as the total mass and radius of the progenitor star, suggest that the
progenitor of GRB 111209A is more likely a Wolf-Rayet star instead of blue
supergiant, and the central engine of this ultra-long burst is a black hole.
The implications of our results is discussed.
