Abstract: In the solution of nonlinear problems, Runge-Kutta method is used to predict the integral interior point load term in the one-step block precise integration method, resulting in a large amount of calculation. Thusly, an improved single step block precise integration algorithm is proposed. The Duhamel integration part and the interior point load prediction part are calculated with refined matrix vector operations through the subblock subdivision calculation. By avoiding the operation of zero and identity matrices, and by storing the calculation results of constant matrix in advance, the calculation complexity is reduced by approximately 20%, only the calculation form changed, and the accuracy is consistent with the original algorithm. The single step block precise integration method improved is applied to the rotor system with nonlinear support to calculate the nonlinear dynamic response of the rotor, and the results are compared with those obtained by the original single step block precise integration method and by Newmark method used widely. Meanwhile, the reliability of the algorithm improved is verified by using experimental results. The result shows that the computational efficiency of the one step block precise integration method improved is significantly improved, compared with the original one step block method. In the complex model calculation example, the accuracy of the single step block precise method improved has similar to that of Newmark method below the speed of 30000 r/min, is significantly higher than that of Newmark method above the speed of 30000 r/min, and has advantages in calculation efficiency. Besides, the consistency between simulation and experimental results proves the effectiveness and reliability of the algorithm improved.