In view of the difficulty of achieving high sensitivity and good stability at the same time for fiber current sensors, mathematical models of straight-through and reflective all-fiber current sensors based on Jones matrix are set up in theory according to Faraday effect. The simulation is conducted by the OptiSystem software, and the linear sensitivities of straight-through and reflective all-fiber current sensors are 0.24 and 0.37. A fiber loop ring-down structure is proposed, and the intensity modulation is converted into the time modulation. The effects of light source and external environment on the performance of system are eliminated, so the system can achieve high sensitivity and good stability at the same time. The scheme is verified in theory and experiment.