Abstract The accuracy of travel time information given to passengers plays a key role in the success of any Advanced Public Transportation Systems (APTS) application. In order to improve the accuracy of such applications, one should carefully develop a prediction method. A majority of the available prediction methods considered the variation in travel time either spatially or temporally. The present study developed a prediction method that considers both temporal and spatial variations in travel time. The conservation of vehicles equation in terms of flow and density was first re-written in terms of speed in the form of a partial differential equation using traffic stream models. Then, the developed speed based equation was discretized using the Godunov scheme and used in the prediction scheme that was based on the Kalman filter. From the results, it was found that the proposed method was able to perform better than historical average, regression, and ANN methods and the methods that considered either temporal or spatial variations alone. Finally, a formulation was developed to check the effect of side roads on prediction accuracy and it was found that the additional requirement in terms of location based data did not result in an appreciable change in the prediction accuracy. This clearly demonstrated that the proposed approach based on using vehicle tracking data is good enough for the considered application of bus travel time prediction.