A magnetic field sensing apparatus including a magnetic flux concentrator, a plurality of magnetoresistance units, and a plurality of magnetization direction setting elements is provided. The magnetic flux concentrator has a top surface, a bottom surface opposite to the top surface, and a plurality of side surfaces connecting the top surface and the bottom surface. The magnetoresistance units are respectively disposed beside the side surfaces. The magnetoresistance units are electrically connected to form an unchangeable Wheatstone full bridge. The magnetization direction setting elements set the magnetization directions of the magnetoresistance units into three different combinations in three different periods, respectively, so as to enable the unchangeable Wheatstone full bridge to respectively measure the magnetic field components in the three different directions in the three different periods.