In the paper, under 5.6 GPa and 1200-1400℃, the type Ib diamond single crystals on defect-free[111] -oriented seed crystals are synthesized in a cubic anvil under high pressure and high temperature when the crack problem of diamond single crystal appears frequently. Highpurity Fe-Ni-Co solvents are chosen as the catalysts. Highpurity graphite powder (99.99%, purity) is selected as a carbon source. The effects of cooling process on the qualities of Gem-diamond single crystals are studied carefully. First, in order to study the common crack defects of diamond single crystals, using scanning electron microscope (SEM), the surface morphologies of high quality diamond single crystals and crack crystals are obtained respectively. Our SEM test results show that the surfaces of the crack crystals and the high quality crystals are all very smooth. Therefore, the crack crystal problem is not directly caused by the unordered accumulation of carbon. Second, the concentrations of nitrogen in the high quality diamonds and crack crystals are measured by Fourier transform infrared. In our studies, the nitrogen content of the diamond single crystal with crack is similar to the nitrogen content of high quality single crystal, so the appearance of crystal crack is not caused by high impurity content. According to the test results and the regularity of the occurrence of crack crystals, the reasons for the occurrence of crack crystals are analyzed seriously. When the weather conditions such as seasonal change, wind, rain or snowfall are not very stable, the probability of crack crystal problem to appear will increase greatly. In our opinion, the decrease of diamond crystal quality caused by the fluctuation of external growth conditions is the internal cause of crack crystal problem appearing. After growing diamond crystals, choosing the traditional power failure mode and slowing cooling process respectively, the effect of cooling process on the quality of diamond single crystal is investigated. In the season of the crack problem occurring frequently, choosing power failure cooling process, cracks appear in both diamond crystals with 1.3 mm or 6.0 mm in diameter. With the slow cooling process, the synthetic diamond crystals with 1.2 mm or 5.8 mm in diameter are all high-quality single crystals with no cracks inside. The research results show that the slow cooling process can effectively restrain the occurrence of crack crystal problems. In addition, the mechanism problems of crack crystals and the mechanisms of the effects of slow cooling process on diamond crystal qualities are discussed in detail. We believe that the slow cooling process is effective in solving the crack crystal problem, which is mainly attributed to the following two aspects:on the one hand, the slow cooling makes the internal stress of diamond single crystal growing effectively released, which improves the compressive strength of the crystal and the crystal quality as well; on the other hand, the slow cooling makes the solidification process of the catalyst melt slowly, which provides enough time for the crystal to balance the external stress of the catalyst and the equipment, so that the crystals, which are not affected by the unbalanced external stress, are not cracked.