We propose a general prediction method based on the efficient computation and online update of the Singular Value Decomposition (SVD) of historical data. The SVD is fundamental to many data modeling algorithms, but the traditional methods for computing it require large computational costs. By adopting a fast sequential SVD updating scheme, the tasks of prediction, imputation of missing values, and model updating can be performed very quickly. In this paper, an application of our method to route travel time prediction is described. Using real travel time data from short sections (links) on expressway, we evaluated prediction performance of travel time on longer section (route) including the links. Experimental comparisons with several statistical machine learning methods suggest that our linear prediction method can achieve similar prediction performance (prediction error) to other nonlinear methods at less computaional cost.