Quartz fiber reinforced silica ceramic matrix composites (SiO_2f/SiO₂) exhibit excellent mechanical, dielectric, anti-corrosion and heat-shielding performance. They have gained extensive applications in the aeronautics field such as radar radome and wave-transparent antenna window. However, because of the ceramic matrix brittleness as well as material anisotropy and inhomogeneity, it becomes difficult to control the machined surface quality. Moreover, grinding itself is also chartered by a complex and highly non-stationary process. How to predict grinding quality for such complex material attracts more research interest. As well known, physics signals generate with the grinding process and have a high correlation with machining quality. Power monitoring is an easy and convenient way to obtain useful information for the grinding process at relative low cost. But analysis in time domain will cause a lot of useful information being ignored. Therefore, it is essential to investigate the feature extraction method in the frequency domain and build the relationship between grinding signal and the surface quality. After fast Fourier transform (FFT), the frequency components, average, maximum and amplitude values in each frequency band are obtained. In this work, 75 groups of grinding experiments were carried on, considering the wheel speed, workpiece feed speed and grinding depth of cut. And the power signals were collected from a developed portable power monitoring system. The frequency domain characteristics of workpiece surface texture and power signals were analyzed to find the relationship between them. A prediction model of surface texture based on the frequency domain characteristics analysis and the correlation analysis was established using BP neural network. The results show that spectrum analysis of monitored power signals could predict the grinding surface quality well.