A gold coated carbon nanotubes composite was used as a contact material in Micro-Electrical-Mechanical-System (MEMS) switches. The switching contact was tested under typical conditions of MEMS relay applications: load voltage of 4 V, contact force of 1 mN, and load current varied between 20-200 mA. This paper focuses on the wear process over switching lifetime, and the dependence of the wear area on the current is discussed. It was shown that the contact was going to fail when the wear area approached the whole contact area, at which point the contact resistance increased sharply to three times the nominal resistance.