Abstract: Navigation system, which can improve an accuracy of a travel distance calculation and an accuracy of present position detection even if an accuracy of a pulse data from a vehicle speed sensor is relatively low. The navigation system includes a gyroscope, a vehicle speed sensor and a navigation control portion. The navigation control portion calculates the travel direction based on outputs from the gyroscope and the vehicle speed sensor. When the vehicle decelerates, acceleration during low speed less than Vmin, in which the vehicle speed pulse is not outputted, is assumed to be equal to an acceleration just before the vehicle speed becomes less than Vmin. When the vehicle accelerates, acceleration during low speed less than Vmin, in which the vehicle speed pulse is not outputted, is assumed to be equal to an acceleration just after the vehicle speed becomes to or more than Vmin.