A magnetic field sensor with a new concentrating-conducting magnetic flux structure (CCMFS) is proposed in this paper, using a silicon-on insulator (SOI) Hall element fabricated by complementary metal oxide semiconductor (CMOS) technology as a magnetic sensitive unit. By fixing the CCMFS above the Hall element packaged on a printed circuit board (PCB) based on inner-connect wire bonding technology, a non-magnetized package can subsequently be obtained. To analyze the inner magnetic field vector distribution of the CCMFS, a simulation model was built based on a finite element software, where the CCMFS was processed using Ni-Fe alloys material by a low speed wire-cut electric discharge technology. The test results showed that the measurement of magnetic fields along a sensitive and a non-sensitive axis can be achieved when VDD = 5.0 V at room temperature, with magnetic sensitivities of 122 mV/T and 132 mV/T in a testing range from −30 mT to 30 mT, respectively. This study makes it possible to not only realize the detection of magnetic field, but also to significantly improve the sensitivity of the sensor along a non-sensitive axis.