Disclosed are a method and an apparatus for treating boil-off gas generated in an LNG storage tank of an LNG carrier for transporting LNG in a cryogenic liquid state, the LNG carrier having a boil-off gas reliquefaction plant, wherein an amount of boil-off gas corresponding to a treatment capacity of the reliquefaction plant among the total amount of boil-off gas generated during the voyage of the LNG carrier is discharged from the LNG storage tank and reliquefied by the reliquefaction plant. The boil-off gas treating method and apparatus can maintain an amount of boil-off gas discharged from an LNG storage tank at a constant level by storing in the LNG storage tank, instead of discharging and burning, surplus boil-off gas which has not been returned to the LNG storage tank through the reliquefaction plant among the total amount of boil-off gas generated in the LNG storage tank, and can prevent waste of boil-off gas and save energy by allowing an internal pressure of the LNG storage tank to be increased.