ABSTRACT It is well known that ordinary supernovae (SNe) are powered by 56Ni cascade decay. Broad-lined type Ic SNe (SNe Ic-BL) are a subclass of SNe that are not all exclusively powered by 56Ni decay. It was suggested that some SNe Ic-BL are powered by magnetar spin-down. iPTF16asu is a peculiar broad-lined type Ic supernova discovered by the intermediate Palomar Transient Factory. With a rest-frame rise time of only 4 d, iPTF16asu challenges the existing popular models, for example, the radioactive heating (56Ni-only) and the magnetar +56Ni models. Here we show that this rapid rise could be attributed to interaction between the SN ejecta and a pre-existing circumstellar medium ejected by the progenitor during its final stages of evolution, while the late-time light curve can be better explained by energy input from a rapidly spinning magnetar. This model is a natural extension to the previous magnetar model. The mass-loss rate of the progenitor and ejecta mass are consistent with a progenitor that experienced a common envelope evolution in a binary. An alternative model for the early rapid rise of the light curve is the cooling of a shock propagating into an extended envelope of the progenitor. It is difficult at this stage to tell which model (interaction+magnetar + 56Ni or cooling+magnetar + 56Ni) is better for iPTF16asu. However, it is worth noting that the inferred envelope mass in the cooling+magnetar + 56Ni is very high.