This paper optimally designs a hollowcore inductive sensor with bandwidth range from 1 Hz to 10 kHz. Firstly, we utilize a magnetic core with hollow structure, and analyze demagnetizing factor and efficient magnetic permeability of hollow core. The magnetic flux of hollow core sensor coil is simulated and measured, and is found equal to the one of rod core sensor coil with the same ratio of length and diameter. Then, sensitivity and noise of inductive magnetic sensor with hollow core are analyzed and the performances of low noise and low weight are achieved by optimizing the noise formula using mathematic algorithm. To verify the theoretical analysis, this paper designs an inductive magnetic sensor with hollow core and tests the performance of the inductive magnetic sensor with hollow core in shielded environment yielding sensitivity of 0.73 V/nT corresponding the frequency higher than 400 Hz and noise of 0.06 pT/Hz1/2 at frequency of 100 Hz. Under this condition, the whole configuration weighs 80 g. The process is consistent with the theoretical analysis. Compared with THEMIS, the inductive magnetic sensor with hollow core has merits of low noise and light weight, and can satisfy the needs of Space Electromagnetic Science.