When a WLAN station has low battery-power, a normal power-saving mechanism is not desirable and sparse wake-up should be used. In that case, the station cannot remain awake throughout every delivery-traffic-indication-message (DTIM) interval, which results in the loss of broadcast and multicast packets. In this letter, we propose a double-buffering power-saving mechanism for stations with low battery power. Broadcast and multicast packets can be delivered to stations with low battery power more reliably with the new scheme.