Abstract: Grinding flutter was a strong vibration between the grinding wheel and the workpiece, which reduced the surface quality of the workpiece and accelerated the wear of the grinding wheel. The stability of machining process was used to solve this problem as the key. Firstly, the grinding experiment platform was built, and the state vector was defined, concurrently, the differential equation was solved by the Runge-Kutta method, which was studied to find the influence of different parameters on machining stability. Secondly, BK7 glass was regarded as an example, the points of stability or instability of feed speed and grinding wheel length was selected for experiments. Finally, Matlab was used to generate time domain signal diagram and power spectrum diagram with the collected data. For feed speed, the peak values of time domain signal diagram and power spectrum of unstable region points were as high as 0.620 2 mm and 0.128 5 dB respectively, while the peak values of stable region points were only 0.295 4 mm and 0.009 9 dB. For the length of grinding wheel, the time domain signal and power spectrum peaks of unstable region points were as high as 2.011 9 mm and 0.160 4 dB, respectively, while the peaks of stable region points were only 0.225 8 mm and 0.006 9 dB.The flutter condition can be judged by analyzing the time-domain signal diagram, and the energy change law can be found by observing the power spectrum diagram. Both of them were used to determine the stable state of the system, at the same time, guide the reasonable selection of machining parameters, and effectively reduce the machining flutter.