As metal boring bars have low dynamic stiffness, chatter is easily induced during the boring process. Therefore, improvement of the chatter stability is an open problem that requires further study. Though researchers proved that the composite materials suitable for making tapered boring bars can further improve the dynamic stiffness to meet the need of high-speed boring, existing research studies did not study the dynamic characteristics of the tapered composite boring bar comprehensively. In particular, no research has been done about the natural frequency and chatter stability of the composite boring bar under various taper ratios. Therefore, in this paper, a model of a tapered composite boring bar is established based on the Adomian modified decomposition method (AMDM). Second, this paper verifies the effectiveness of the AMDM by using the ANSYS software. Moreover, this paper studies the natural frequency of the boring bar model under various situations. Third, we verify the convergence of chatter stability of the boring bar model. Finally, the chatter stability of the tapered composite boring bar is analyzed comprehensively. The results show that the natural frequency and the chatter stability of the tapered model can be improved by choosing appropriate taper ratio, ply angle, stacking sequences, L/D ratio, T/D ratio, and the carbon composite. The results are helpful for the design of high-quality tapered composite boring bars matching the need of high speed cutting. In particular, these results can provide guidelines for adjusting the cutting speed in CNC boring and can further improve the surface finish of the machined workpieces.