A geomagnetic field is a vector field in which the strength and direction are related to geographical location. Geomagnetic navigation technology, which uses collected geomagnetic field information to achieve positioning and navigation, has the advantages of reliability, stability, accuracy, and concealment. With the deepening research on geomagnetic navigation, bioinspired geomagnetic navigation technology has also been developed, which mainly studies and imitates the magnetic sensing mechanism and navigation behavior of animals, providing new research ideas for geomagnetic navigation technology. The magnetic particle hypothesis and free radical pair hypothesis are two mainstream mechanisms of biological sensing using the geomagnetic field, and studies have shown that these two mechanisms may be coupled within organisms. In this study, we propose a bioinspired weak magnetic vector (BWMV) sensor based on the joint sensing mechanism of magnetic particles and free radicals. It consists of a magnetic rod made of soft magnetic material and a tunnel magnetoresistance (TMR) sensor array. A magnetic rod was used to simulate magnetic particles to convert magnetic field angle information into magnetic field intensity distribution information, and the TMR sensor array was used to simulate the perception of the magnetic field distribution by free radicals. In addition, artificial neural networks (ANNs) were used for BWMV sensors to obtain the mapping relationship between the magnetic field distribution and parameters, which can be used for geomagnetic navigation. To verify the navigation effect of the BWMV sensor in the laboratory, a simulated geomagnetic navigation device was built, and the high-precision mapping relationship from geomagnetic parameters to latitude and longitude information of the selected navigation area was obtained through another ANN. Finally, the effectiveness of the BWMV sensor based on ANNs for geomagnetic navigation is verified using simulated navigation experiments.