In order to accurately forecast quality of service (QoS) of different Web services with multi-step, and help users to choose the most suitable Web service at hand, this study proposes a novel QoS forecasting approach called MulA-LMRBF (multiple-step forecasting with advertisement by levenberg-marquardt improved radial basis function network) based on multivariate time series. Considering the correlation among different QoS attributes series, phase-space reconstruction is used to map historical multivariate QoS data into a dynamic system, where the multi-dimensional nonlinear relations of QoS attributes are completely restored. Average dimension (AD) is used to estimate the embedding dimension and delay time of reconstructed phase space. The short-term QoS advertisement data of service provider is also added to form a more comprehensive data set. Then, RBF (radial basis function) neural network improved by the Levenberg-Marquardt (LM) algorithm is used to update the weight of the neural network dynamically, which improves the forecasting accuracy and realizes the dynamic multiple-step forecasting. Experiments are conducted based on several public network data sets and self-collected data set. The experimental results demonstrate that MulA-LMRBF is better than previous approaches with high precise and is more suitable for multi-step forecasting.