The spin polarization of carbon nanotubes (CNTs) offers a tunable building block for spintronic devices and is also crucial for realizing carbon-based electronics. However, the effect of chiral CNTs is still unclear. In this paper, we use the density functional theory (DFT) method to investigate the spin polarization of a series of typical finite-length chiral CNTs (9, m). The results show that the spin density of chiral CNTs (9, m) decreases gradually with the increase in m and vanishes altogether when m is larger than or equal to 6. The armchair edge units on both ends of the (9, m) CNTs exhibit a clear inhibition of spin polarization, allowing control of the spin density of (9, m) CNTs by adjusting the number of armchair edge units on the tube end. Furthermore, analysis of the orbitals shows that the spin of the ground state for (9, m) CNTs mainly comes from the contributions of the frontier molecular orbitals (MOs), and the energy gap decreases gradually with the spin density for chiral CNTs. Our work further develops the study of the spin polarization of CNTs and provides a strategy for controlling the spin polarization of functional molecular devices through chiral vector adjustment.