A power saving method applied to a central processing unit under a non-snooping sleeping state with a bus master request from a peripheral device is presented. In accordance with the present invention, first prohibit the central processing unit from fetching instruction. Then drive the central processing unit entering a snooping sleeping state and enabling the arbiter for transferring the bus master request to the central processing unit. After the central processing unit completes the bus master request, the arbiter is disabled and the central processing unit is driven to leave the snooping sleeping state and return back to the non-snooping sleeping state. Therefore, the power consumed by the central processing unit is reduced so as to save power.