1. A firmware variable update method, for a Basic Input/Output System (BIOS) of a computer system, comprising: writing an update capsule file and a firmware update command into a memory according to a first system management interrupt signal and performing a shutdown process, wherein the firmware update command is utilized for indicating performing a capsule file updating process; triggering a second system management interrupt signal and accordingly writing a variable update command into the memory, wherein the variable update command is utilized for indicating performing a firmware variable updating process; switching the computer system into a sleep state before the shutdown process is completed and activating a timer; performing a first reboot process when the timer expires; utilizing the update capsule file to update an original capsule file of the BIOS according to the firmware update command during the first reboot process; and performing a second reboot process and utilizing an update variable file to update an original variable file of the BIOS according to the variable update command during the second reboot process.