Large residual stress occurs during the quenching process of hot-rolled seamless steel tubes, which results in bending, cracking, and ellipticity exceeding standards and seriously affects the quality of hot-rolled seamless steel tubes. In addition, the stress generation mechanism of hot-rolled seamless steel tubes is different from that of steel plates due to the characteristics of annular section. In this research, the finite element simulation method was used to study the quenching residual stress of seamless steel tubes with different cooling intensities. The variation law of temperature and stress on the steel tube under different cooling intensities were analyzed. The results show that the radial stress was close to 0, and the circumferential and axial stresses were the main factors affecting the quality of the steel tube. With the increase in the cooling time, the magnitude and direction of each stress component of the steel tube changed simultaneously. Finally, a typical stress distribution state of “external compressive stress, internal tensile stress” was presented in the thickness direction of the steel tube. Furthermore, with the increase in the cooling intensity, the residual stress of the steel tube gradually increased and was mainly concentrated on the near wall of the steel tube.