A leakage current measurement apparatus for measuring leakage currents is disclosed. The leakage current measurement apparatus automatically selects one of non-inductive shunt resistors of 10Ω, 100Ω, and 1000Ω and measures leakage currents of an outdoor isolation material for an ultra-high voltage. Additionally, the leakage current measurement apparatus is capable of measuring a relatively wide range of leakage currents with a relatively high precision, even at a remote location, as a measurement range is automatically adjusted within measurement ranges preset by a user when leakage currents of an outdoor isolation material change, and being protected against a surge possibly generated by an ultra-high voltage. Also, it can remotely measure in real-time leakage currents of an outdoor isolation material installed at a remote location over Ethernet.