The technology of satellite orbit prediction (OP) is crucial in space engineering. However, it is difficult to precisely predict medium and long-term orbit for the low Earth-orbit (LEO) satellites because of time-varying space weather and inaccurate atmospheric density models. To address the problem, a novel intelligent OP method based on the variational mode decomposition-support vector machine (VMD-SVM) framework is presented. First, the concept of a pseudo-drag coefficient is defined, transforming the OP problem into a pseudo-drag coefficient prediction problem. Second, the relationship between space weather parameters and the pseudo-drag coefficient is analyzed using the VMD method, from which a strong correlation is shown. Furthermore, an SVM model combined with space weather characteristic parameters is employed to predict the pseudo-drag coefficient, significantly improving the precision of OP when further integrated into the orbital dynamics model. Experiments with data from engineering applications show that VMD-SVM medium and long-term OP technology is practical and effective.