A traveling direction measuring apparatus including 3-axes acceleration detecting means for detecting acceleration, and acceleration data acquiring means for repeatedly obtaining 3-axes acceleration data, said 3-axes acceleration varying with walking of a pedestrian, the traveling direction measuring apparatus including means for calculating, when the pedestrian is walking with holding said traveling direction measuring apparatus in a generally fixed attitude, gravity acceleration by averaging acceleration data sets during several steps obtained by said acceleration data acquiring means, means for calculating frequency components corresponding to duration of one step of the acceleration data sets projected on a plane perpendicular to the calculated gravity acceleration, and means for estimating a moving direction of the pedestrian seen from a terminal coordinate system associated with said traveling direction measuring apparatus according to frequency components.