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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 toinvestigate the physics of central engines or even progenitors for ultra-longGRBs. 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 withfall-back accretion for GRB 111209A/SN 2011kl. The required model parameters,such as the total mass and radius of the progenitor star, suggest that theprogenitor of GRB 111209A is more likely a Wolf-Rayet star instead of bluesupergiant, and the central engine of this ultra-long burst is a black hole.The implications of our results is discussed.

Black hole central engine for ultra-long gamma-ray burst 111209A and its associated supernova 2011kl