Magnetoelectric (ME) composites have been proved to be applicable to current sensors. However, the previously reported ME materials-based current sensors mainly focus on direct current and sine alternating current sensing, which put a critical limit on the measurement of transient current. In this paper, a cylindrical ME composite consisting of a magnetostrictive Fe83Ga17 (FeGa) cylinder and a piezoelectric Pb(Zr,Ti)O3 (PZT) circular tube is fabricated for lightning current sensing applications. The time-domain output voltage of the FeGa/PZT composite is simulated and measured in detail. Under the excitation of 8/20µs lighting current, the output voltage of the composite can change with the current. But the damping oscillation at its resonant frequency is observed. Furthermore, to obtain an obvious ME response, the FeGa/PZT cylinder and current-carrying wire should be arranged closely and in an orthogonal way. When the amplitude of 8/20µs lightning current is in the range of 500A to 9kA, the ME FeGa/PZT composite shows a sensitivity of 1.36mV/A, a linear response (R2=0.9993), and a small return error (0.12V). These results provide that the ME composite is suitable to be used in non-contact lightning current measurement.