To accurately analyze dynamic characteristics of pointing mechanism of a CO2 space spectrometer, a bearing finite element contact analysis model was established according to the bearing structural parameters in this paper. The displacements with different loads for an axis were calculated, and the nonlinear stiffness curve for the bearing was obtained by the polynomial fitting for calculated results. In finite element dynamic analysis model of pointing mechanism, a spring unit with corresponding stiffness was used to replace the bearing structure, and the dynamic characteristics of the pointing mechanism were obtained by analysis of infinite element frequency response. The simulation experiment shows that the surface shape of mirror is 19.23 nm and 19.27 nm in optics axis and meridian direction at a static condition, which satisfy the design requirement of λ/30(RMS, λ=632.8 nm) and all base frequencies in 3 directions are over 100 Hz. Moreover, mechanical vibration experiments also verify that all base frequencies in 3 directions are over 100 Hz and the surface shape accuracy of the mirror is λ/35. The calculation results agree well with the experimental results. It concludes that the analysis method with nonlinear contact solves the bearing stiffness accurately, and the static/dynamic performance of pointing mechanism meets design requirements.