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We report the experimental observation and micromagnetics simulation of the current-induced switching of the magnetic vortex core in ferromagnetic elliptical disks. We found that the critical current density required for the core switching depends on the relative alignment between the current direction and the elliptical axes of the disk. The micromagnetics simulation results qualitatively reproduce the experimental findings, suggesting that the vortex core displacement induced by the current plays a significant role for the core switching rather than the core velocity.