For the accuracy of the predictive models for single input single output (SISO) and multiple input multiple output (MIMO) nonlinear time-delay systems, the schemes of constructing predictive models based on the multi-dimensional Taylor network (MTN) are proposed. First, the non-recursive direct d-step-ahead MTN predictive model and the recursive d-step-ahead MTN predictive model are designed and the expressions are given respectively relying on non-recursive and recursive technology, which can predict the range of d steps in the future and compensate the influence of time-delay. Then the damped recursive least squares (DRLS), the BP algorithm with momentum factors, the Levenberg Marquardt (L-M) and the extended Kalman filter (EKF) learning algorithms are used as the learning of the MTN predictive model to conduct on-line learning, respectively. Finally, two experimental examples are given to certify the accuracy and real-time performance of the predictive model, which are compared with those of the neural network predictive models. Results from our experiments show that the two kinds of predictive models constuctedusing the proposed schemes have a better accuracy and real-time performance than the neural network predictive models. Meanwhile, four kinds of different learning algorithms have little effect on the accuracy of the MTN predictive models.