The Lyman-Kutcher-Burman (LKB) normal tissue complication probability (NTCP) model is often used to estimate the damage level to normal tissue. However, it does not manifestly involve the influence of radiosensitivity parameters. This work replaces the generalized mean equivalent uniform dose (gEUD) with the equivalent uniform dose (EUD) in the LKB model to investigate the effect of a variety of radiobiological parameters on the NTCP to characterize the toxicity of five types of radionuclides. The dose for 50 % complication probability (D (50)) is replaced by the corresponding EUD for 50 % complication probability (EUD(50)). The properties of a variety of radiobiological characteristics, such as biologically effective dose (BED), NTCP, and EUD, for five types of radioisotope ((131)I, (186)Re, (188)Re, (90)Y, and (67)Cu) are investigated by various radiosensitivity parameters such as intrinsic radiosensitivity α, alpha-beta ratio α/β, cell repair half-time, cell mean clonogen doubling time, etc. The high-energy beta emitters ((90)Y and (188)Re) have high initial dose rate and mean absorbed dose per injected activity in kidney, and their kidney toxicity should be of greater concern if they are excreted through kidneys. The radiobiological effect of (188)Re changes most sharply with the radiobiological parameters due to its high-energy electrons and very short physical half-life. The dose for a probability of 50% injury within 5y (D (50/5)) 28 Gy for whole-kidney irradiation should be adjusted according to different radionuclides and different radiosensitivity of individuals. The D (50/5) of individuals with low α/β or low α, or low biological clearance half-time, will be less than 28 Gy. The 50 % complication probability dose for (67)Cu and (188)Re could be 25 Gy and 22 Gy. The same mean absorbed dose generally corresponds to different degrees of damage for tissues of different radiosensitivity and different radionuclides. The influence of various radiobiological parameters should be taken into consideration in the NTCP model.