The present invention relates to a traveling direction measuring apparatus usable as a pedestrian navigation system in locations where it is difficult to obtain high positioning accuracy such as inside buildings or around multistory buildings where a GPS cannot be used. An acceleration detecting section (1) detects 3-axes acceleration of the traveling direction measuring apparatus, which varies with the walking of the pedestrian. An acceleration data acquiring section (2) obtains 3-axes acceleration data repeatedly by the number of prescribed times or more, said 3-axes acceleration data varies with the walking of the pedestrian. A first gravity acceleration calculating section (3) calculates, when the pedestrian is walking with holding the traveling direction measuring apparatus in a generally fixed attitude, gravity acceleration by averaging acceleration data sets during several steps obtained by the acceleration data acquiring section (2). A first moving direction estimating section (4) estimates the moving direction of the pedestrian from frequency components corresponding to the duration of one step of the acceleration data sets projected on a plane perpendicular to the gravity acceleration calculated by the first gravity acceleration calculating section (3).