Method and memory card system for supplying power with a memory card of the memory card system

A method and a memory card system for supplying power to a memory card of the memory card system are provided to guarantee execution of background tasks after a write operation by enabling the memory card to know a cut-off time point of the power supplied from a host. A memory card(220) stores data, and a host(210) detects a time point completing a write operation of the memory card and generates a power-off strobe signal to the memory card after a predetermined time is passed from the detected write complete time point. The host cuts off power supplied to the memory card after a predetermined power-off delay time until the power-off strobe signal is generated to the memory card, and the host detects the write complete time point based on a busy signal of the write operation.