Magnetically induced optical transparency (MIOT) is a technique to realize the narrow transmission spectrum in a cavity quantum electric dynamics (cavity QED) system, which is demonstrated in the recent experiment of cold 88Sr atoms in an optical cavity [Phys. Rev... Lett. 118, 263601 (2017)]. In this experiment, MIOT induces a new narrow transmission window for the probe beam, which is highly immune to the fluctuation of the cavity mode frequency. The linewidth of this transmission window approaches the decay rate of the electronic 3P1 state (about 2pi*7.5kHz) and is much less than the uncertainty of the cavity mode frequency (about 2pi*150kHz). In this work, we propose an approach to further reduce the linewidth of this MIOT-induced transmission window, with the help of two Raman beams which couples the electronic 3P1 state to the3S1state, and the3S1state to the 3P0 state, respectively. With this approach, one can reduce the transmission linewidth by orders of magnitude. Moreover, the peak value of the relative transmission power or the transmission rate of the probe beam is almost unchanged by the Raman beams. Our results are helpful for the study of precision measurement and other quantum optical processes based on cavity quantum electronic dynamics (cavity-QED). (read more)