Metal-matrix diamond composites have been extensively used and studied, but vacancies, doping, and other defects caused by the pretreatment of the diamond surface significantly affect the interface property between the metal base and diamond. Although techniques like transmission electron microscopy and spectroscopy analysis have been used to detect defects, they present certain limitations. Calculating the positron annihilation lifetime in diamond provides an accurate assessment of interface defect in the diamond. This study uses first-principles calculation methods and adopts various positron annihilation algorithms and enhancement factors, to compute the positron annihilation lifetimes in ideal diamond crystals, single vacancies, and diamond crystals doped with B, Cr, Mo, Ti, W, and Zr. The results, obtained by using local density functional in combination with Boronski & Nieminen algorithms and random-phase approximation restriction as annihilation enhancement factors, indicate that the computed positron annihilation lifetime of diamond is 119.87 ps, which is consistent closely with the experimental result in the literature. Furthermore, after B, Cr, Mo, Ti, W, and Zr atoms are doped into diamond (doping atomic concentration of 1.6%), the positron annihilation lifetimes change from a single vacancy 119.87 ps to 148.57, 156.82, 119.05, 116.5, 117.62, and 115.74 ps respectively. This implies that the defects due to doped atoms in diamond change their positron annihilation lifetimes, with the influence varying according to the different atoms doped. Based on the calculated electron density in diamond vacancies and doped atom areas, it is discovered that doping atoms do not cause severe distortion in the diamond lattice. However, after B and Cr atoms are doped, the positron annihilation lifetime increases significantly. The primary reason is that the relatively low positron affinity of B and Cr atoms results in an extended positron residence time in the vacancy, thereby increasing the annihilation lifetime. Overall, vacancies and doped atom defects in diamond will cause its positron annihilation lifetime to change. The above conclusions provide crucial theoretical references for detecting and identifying interface defects caused by doping treatment on the diamond surface during the preparation of metal-matrix diamond composites.