Flapping motion of the current sheet (CS) is an important physical process in the Earth’s magnetotail. The magnetic double- gradient model, which includes both the instability and wave modes, offers a reasonable explanation for the exciting and propagation of the flapping wave. In this paper, we apply an advanced numerical magnetohydrodynamic (MHD) scheme (conservation element and solution element (CESE)-MHD) to simulate the magnetic double-gradient instability in an idealized current sheet that mimics the magnetotail configuration. We initialize the simulations with a numerically relaxed magnetotail equilibrium, in which the normal component of the magnetic field has a tailward gradient. It is confirmed in our simulation that the instability develops in the current layer. The growth rate of the instability yielded from the simulation is very close to the prediction of theory, with a relative deviation of only ten percent. The results demonstrate that the CESE-MHD scheme is very powerful in numerical study of the double-gradient mechanism of the CS flapping mode, and can be used for further investigations of the flapping motion in more realistic CS configurations. © 2018, Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature.