A magnetic field sensing apparatus including a magnetic flux concentrator, a plurality of single direction magneto-resistive sensors and a time division switching circuit is provided. The magnetic flux concentrator has a plurality of corners. The single direction magneto-resistive sensors have a same pinning direction. The single direction magneto-resistive sensors are respectively disposed beside the corners. The time division switching circuit is coupled to the single direction magneto-resistive sensors, and is configured to switch at least a portion of the junctions between the single direction magneto-resistive sensors to change a circuit connection between the magneto-resistive sensors, thereby forming different Wheatstone bridges being configured to measure different magnetic field components of the external magnetic field in different directions.