1. An optical disc drive having a normal operation mode and a firmware update mode, the optical disc drive comprising: a firmware memory; a buffer memory; a processor electrically connected to the firmware memory, for controlling the optical disc drive to fetch an update firmware from an optical disc and store the update firmware into the buffer memory when the optical disc drive is under the normal operation mode; and a memory update controller electrically connected to the firmware memory and the buffer memory, for fetching the update firmware from the buffer memory and storing the update firmware into the firmware memory when the optical disc drive is under the firmware update mode without the processor executing an update routine code for updating firmware stored in the firmware memory.