Some industrial incidents are attributed to insulation degradation of electrical assets. The leakage current can be a crucial indicator for online insulation monitoring of asset. To realize per-phase monitoring, the measurement accuracy of milliampere-level leakage current is limited by the strong load current noises. This paper proposes an advanced current sensor with a dual-core topology based on differential-mode (DM) measurement. An analytical model of magnetic field of the dual-core sensor is originally presented. It helps clarify the significances of the inner core in filtering noises and reducing the influence of system operation and cable positioning. Then, a comprehensive design procedure is fully investigated by selecting the optimal position and approach for magnetic field detection, and a high-speed and low-noise signal conditioning circuit is presented. The proposed current sensor is tested in the laboratory. Experimental results indicate that measurement errors can remain within 0.1mA in the testing scope, where the load current is up to 100A and the DM current varies from 0-7mA. The proposed sensor is further validated with superior performance compared with two commercial industrial sensors. The contribution of this paper lies in providing the analytical analysis and design of a novel DM current sensor for leakage current measurement, which achieves online per-phase insulation monitoring for industrial electrical assets.