A display apparatus and an operation method thereof are provided. The display apparatus includes: a volatile memory; a nonvolatile memory; and a processor configured to: determine stability of a system for the display apparatus; when a power-off input for the display apparatus is received, if the system is determined to be stable, enter a power-saving mode while maintaining power supply to the volatile memory in which execution data regarding an application currently being executed is stored; and if the system is determined to be unstable, perform power-off processing after storing execution status information of at least one application being executed in the nonvolatile memory, perform booting to execute the application by using application execution status information stored in the nonvolatile memory, and store the execution data regarding the executed application in the volatile memory and then enter the power saving mode while maintaining the power supply to the volatile memory.