Prediction of travel time on road network has emerged as a crucial research issue in intelligent transportation system (ITS). Travel time prediction provides information that may allow travelers to change their routes as well as departure time. To provide accurate travel time for travelers is the key challenge in this research area. In this paper, we formulate two new methods which are based on moving average can deal with this kind of challenge. In conventional moving average approach, data may lose at the beginning and end of a series. It may sometimes generate cycles or other movements that are not present in the original data. Our proposed modified method can strongly tackle those kinds of uneven presence of extreme values. We compare the proposed methods with the existing prediction methods like Switching method 10 and NBC method 11. It is also revealed that proposed methods can reduce error significantly in compared with other existing methods.