In a liquid rocket turbopump with low pressure and thin wall tanks, cavitation inevitably occurs at the inducer which is installed at the inlet of the turbopump. The cavities at each blade oscillate periodically, and the turbopump sometimes becomes unstable, called cavitation instability. Rotating cavitation is one of the common types of cavitation instability, in which the cavities at each inducer blade oscillate respectively and appear to propagate from blade to blade. However, the new type of cavitation instability which does not follow the conventional principle has been observed in our experiment with an inducer. Converting the frequency in the inertial frame to that in the rotational frame and organizing it in the cavitation number, it was found that the frequency of unsteady cavitation increases as the cavitation number decreases, and this is the peculiar point of this instability. Additionally, during the cavitation instability, a few numbers of backflow vortex cavities were observed and moved sub-synchronously from blade to blade. In addition, the tip leakage vortex cavitation on each blade also propagates like sub-synchronous rotating cavitation but in different propagation speed from that of the backflow vortex cavities. As a result, it was supposed that the new instability is one of the types of sub-synchronous rotating cavitation related to backflow vortex cavitation, tip leakage vortex cavitation, and interaction between cavity propagation and inducer blade.