In this paper, a slot microring with an asymmetric grating structure is proposed. Through the coupling between the grating and the slot microring, a high free spectral range or EIT-like effects with a high quality factor can be achieved in the same device. The grating is designed as an asymmetric structure to realize the modulation of the optical signal and the control of the resonance peak by changing the grid number, and the effect of different grating periods on the output spectrum is explored. The results show that changing the grating on slot sidewalls can increase or decrease the number of resonant peaks. By selecting a specific period of the gratings on both sides of the slot, the distance between adjacent resonance peaks can be increased to achieve modulation of the free spectral range. In this paper, depending on the grating period, we obtain a quality factor of 5016 and an FSR of 137 nm, or a quality factor of 10,730 and an FSR of 92 nm. The refractive index sensing simulation is carried out for one of the periods, which can achieve a sensitivity of 370 nm/RIU. Therefore, the proposed new structure has certain advantages in different sensing applications.