In a weak-magnetic field sensor a rectangular ring-shaped magnetic core is wound by exciting circuit patterns and detecting circuit patterns, and weak-magnetic field sensors are implemented in x-axis and y-axis directions, respectively, to precisely calculate azimuth, thereby sensing a weak-magnetic field having a strength similar to that of earth's magnetic field. The sensor includes a magnetic core having first and second cores connected in parallel to each other; exciting coils wound around the first and second cores, respectively, to supply alternating excitation current to the magnetic core; and a detecting coil alternately arranged together with the exciting coils on the same surfaces on which the exciting coils are formed, and wound around the first and second cores, in order to detect variation of magnetic fluxes generated in the magnetic core.