Abstract: To improve the efficiency and accuracy of multistep predicting of the time series, a Volterra series model based on the multi recursive affine projection (AP) algorithm is proposed. The optimal embedding dimension is identified by false nearest neighbors to optimize the initial parameters of the model. Taking the minimum norm of the Volterra kernel vector increments and certain constraints as the overall cost function, by the steepest descent principle, the adaptive updating formula of the Volterra kernel vector of each order is derived. And the matrix inverse lemma is applied to recursively estimate the inverse of the autocorrelation  matrix of Volterra subsystems of each order, thus the algorithm is derived. To illustrate the performance of the method, simulations on Henon time series prediction are performed. The results show that the Henon time series are accurately predicted, which demonstrates the effectiveness of the proposed method.