This paper is concerned with the task of travel-time prediction for an arbitrary origin-destination pair on a map. Unlike most of the existing studies, which focus only on a particular link (road segment) with heavy traffic, our method allows us to probabilistically predict the travel time along an unknown path (a sequence of links) if the similarity between paths is defined as a kernel function. Our first innovation is to use a string kernel to represent the similarity between paths. Our second new idea is to apply Gaussian process regression for probabilistic travel-time prediction. We tested our approach with realistic traffic data.