In view of the characteristics of the small amplitude of a current signal, an all-optical fibre small-current sensor for partial discharge is devised. A novel type of sensor head with electric winding light is proposed. A complete optical model of the optical fibre current sensor is developed under the effect of polarization error factors. In addition, the effect of polarization error factors on the optical fibre sensing system is simulated. The simulation results show that as the extinction ratio increases, the output relative error of the optical fibre small-current sensor decreases. The effect of the fast and slow axis misalignment errors of a polarizing beam splitter is similar to the effect of the alignment angle error of an optical fibre polarizer. It is observed that the relative error curve follows a sine function. Meanwhile, the output relative error increases first and then oscillates with an increase in the linear birefringence. We conclude that the linear birefringence of the sensing optical fibre is the main error source for the measurement accuracy of the sensing system. Finally, an experimental system for the optical fibre small-current sensor is implemented. The experimental results show that the effect of linear birefringence on the fibre current sensing system can be suppressed by introducing a large amount of circular birefringence into the sensing optical fibre. The theoretical mechanism of these errors is analysed, which can be applied to implement corresponding measures to reduce the effect of error factors on the sensing system and further improve the measurement accuracy of the optical fibre small-current sensor.