The current monitoring of bundle conductors is essential for precisely locating operation failures in transmission lines, leading to a more stable and reliable power grid. This paper proposed a novel method for current reconstruction of bundle conductors, utilizing tunneling magnetoresistive (TMR) sensors. Both the normal and abnormal situations are discussed. The optimal and sub-optimal measurement points for sensors were obtained for concise current measurement with only one uniaxial TMR sensor. The current in each bundle conductor was calculated separately based on the comprehensive algorithm. Validation experiment indicated the error of the measurement and calculation system was no more than 10%, proving the robustness and feasibility of the measurement system and the algorithm. The reconstruction process takes full advantages of TMR sensors and provides a promising solution for transmission line monitoring in power grid.