Single spin color centers in solid materials are one of the promising candidates for quantum information processing, and attract a great deal of interest. Nowadays, single spin color centers in silicon carbide, such as divacancies and silicon vacancies have been developed rapidly, because they not only have similar properties of the NV centers in diamond, but also possess infrared fluorescence that is more favorable for transmission in optical fiber. However, these centers possess week fluorescence with broad spectrum, which prevents some key technologies from being put into practical application, such as quantum key distribution, photon-spin entanglement, spin-spin entanglement and quantum sensing. Therefore, optical resonator is very suitable for coupling centers to filter their spectrum and enhance the fluorescence by Purcell effect. It is very advantageous to use the fiber end face as cavity mirrors, thereby the fiber can provide small cavity volume corresponding to a large enhancement in spin color centers, and collect the fluorescence in cavity simultaneously, which has no extra loss in comparison with other collection methods. In this work, the properties and performance of fiber Fabry-Perot cavity coupling silicon carbide membrane are mainly studied through theoretical calculation. Firstly, some parameters are optimized such as membrane roughness and mirror reflection by calculating the mode of the fiber cavity and enhancing the color centers coupling into the cavity, then analyzing the properties of different modes in cavity, the enhancement effect on cavity coupling color centers, and other relevant factors affecting the cavity coupling color centers. Next, the influences of dominated factor and vibration on the properties of the cavity, the enhancement and outcoupling of centers coupled into the cavity are investigated, and finally the optimal outcoupling efficiency corresponding to different vibration intensities is obtained. These results give direct guidance for the further experimental design and direction for optimization of the fiber cavity coupling color centers.