In this paper, we propose a multidimensional version of recurrent least squares support vector machines (MDRLSSVM) to solve the problem about the prediction of chaotic system. To acquire better prediction performance, the high-dimensional space, which provides more information on the system than the scalar time series, is first reconstructed utilizing Takens’s embedding theorem. Then the MDRLS-SVM instead of traditional RLS-SVM is used in the highdimensional space, and the prediction performance can be improved from the point of view of reconstructed embedding phase space. In addition, the MDRLS-SVM algorithm is analysed in the context of noise, and we also find that the MDRLS-SVM has lower sensitivity to noise than the RLS-SVM.