We study the most luminous known supernova (SN) associated with a gamma-ray burst (GRB), SN 2011kl. The photospheric velocity of SN 2011kl around peak brightness is $21,000pm7,000$ km s$^{-1}$. Owing to different assumptions related to the light-curve (LC) evolution (broken or unbroken power-law function) of the optical afterglow of GRB 111209A, different techniques for the LC decomposition, and different methods (with or without a near-infrared contribution), three groups derived three different bolometric LCs for SN 2011kl. Previous studies have shown that the LCs without an early-time excess preferred a magnetar model, a magnetar+$^{56}$Ni model, or a white dwarf tidal disruption event model rather than the radioactive heating model. On the other hand, the LC shows an early-time excess and dip that cannot be reproduced by the aforementioned models, and hence the blue-supergiant model was proposed to explain it. Here we reinvestigate the energy sources powering SN 2011kl. We find that the two LCs without the early-time excess of SN 2011kl can be explained by the magnetar+$^{56}$Ni model, and the LC showing the early excess can be explained by the magnetar+$^{56}$Ni model taking into account the cooling emission from the shock-heated envelope of the SN progenitor, demonstrating that this SN might primarily be powered by a nascent magnetar.
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