To study the corrosion characteristics of high-strength sucker rods in high-salinity well fluids under alternating stresses, a single-factor stress corrosion test was designed. The slow strain rate tensile test (SSRT) was carried out for four kinds of high-strength sucker rods under different Cl− and HCO3− concentrations and with different service strengths, and the variable stress corrosion cracking susceptibility was analyzed. The results show that the elongation loss and absorbed work loss of the H-grade ultra-high-strength 4330 sucker rod after stress corrosion are greater than those of both the high-strength 4142 sucker rod and the high-strength 20CrMoA sucker rod. The elongation and absorbed work loss of the 30CrMoA and 20CrMoA sucker rods are less affected by the changes in Cl− and HCO3−. With the increase in use strength, the elongation and absorbed work loss of the high-strength sucker rod increase. The change in the surface of the sucker rod during the corrosion process is inconsistent with the actual elongation of the sucker rod and the absorbed work loss. It can be concluded that the stress corrosion cracking susceptibility of the sucker rod is not necessarily related to the tensile strength of the sucker rod. The 4330 sucker rod is not suitable for applications in wells with a high concentration of Cl−, but it is suitable for operation in alkaline conditions where corrosive media such as HCO3− and Cl− coexist. Under highly corrosive and highly mineralized conditions, the 30CrMoA sucker rod is less susceptible to stress corrosion. The stress corrosion cracking susceptibility of the 20CrMoA sucker rod is lower than that of the 4142 sucker rod. In high-salinity well fluids, the higher the use strength, the higher the stress corrosion cracking susceptibility of the high-strength sucker rod is. The test results for the weight-loss-based corrosion rate and plastic loss may contradict the determination of the corrosion susceptibility of the material under working conditions.