The magnon-magnon coupling between two ferromagnetic thin films is usually established by interlayer exchange interaction, which works as a boundary condition and in cases of strong interaction leads to the phenomenon of "anti-crossing". Previous studies have been devoted to ferromagnetic metal/magnetic insulator (FM/MI) bilayers; however, the level of damping in FMs here is usually 1-2 orders of magnitude greater than in MIs, causing a decrease in coherence time. Here, we show, for the first time, a strong coupling with a cooperativity of more than 10 between two MIs with experimentally relevant parameters via the finite element method in the frequency domain, consistent with our numerical method. This anti-crossing coupling in low-damping MI bilayers could pave the way for exciting prospects such as low-energy consumption magnonic devices.