A memory-control circuit for use in an integrated circuit is provided. The memory-control circuit includes a memory controller and a timer circuit. The memory controller performs an erase operation on a target data block of the flash memory according to an erase command from a processor, and generates an erase signal. The timer circuit starts a counting operation in response to the erase signal. In response to an intellectual-property-core circuit generating an interrupt signal, the memory controller and the timer circuit respectively suspend the erase operation and the counting operation. In response to the interrupt signal being cleared, the memory controller and the timer circuit respectively resume the erase operation and the counting operation. In response to the timer circuit having counted up to a predetermined value, the timer circuit outputs a completion signal to the memory controller to indicate that the erase operation is complete.