Traffic engineering (TE) plays an essential role in deciding routes that effectively use network resources. This is particularly important when one considers the increasing time variation of Internet traffic such as streaming and cloud services. Traffic engineering with traffic prediction is one approach to stably accommodating time-varying traffic. This approach calculates routes from predicted traffic to avoid congestion, but predictions may include errors that instead cause congestion. We propose a prediction-based traffic engineering method that is robust to prediction errors by considering the probability distribution of predicted traffic. Our approach is based on a control-theoretic approach called stochastic model predictive control. Routes are calculated using a probability distribution of prediction errors so that the occurrence probability of congestion is lower than an operator-specified level. By considering the multi-step future dynamics of traffic, the routes are changed gradually to avoid route oscillation. We also show a relaxation method for unreliable far-future probabilistic constraints to avoid overly conservative route changes. Through simulations using backbone network traffic traces, we demonstrate that our method can accommodate most traffic variations under a given target link capacity without sudden large routes changes.