Under the reactor neutron irradiation, the point defects and their evolution in zirconium alloys will affect its mechanical properties. At present, the mechanism of the effect of irradiation defects on the mechanical properties of Zr-Nb binary system is still unclear. Therefore, based on the density functional theory, the effects of point defects and Nb-doping on the mechanical properties of α-Zr are studied using first principles method. The results show that vacancy increases the shear modulus while Nb-doping decreases the shear modulus of α-Zr. It is found that the introduction of point defects will weaken the anisotropy of α-Zr structure by calculating the three-dimensional Young"s modulus of α-Zr with different configurations of point defects, so it can be predicted that single point defects are helpful to alleviate the degradation of irradiation properties of zirconium alloys.