In this paper we present an adaptive application-driven power management (AADPM) strategy with online idle period length distribution learning capability for the IEEE 802.11b WLAN. We discuss its design and evaluate the performance in comparison with other power management strategies using the network simulator NS2. We simulated both the single user and multiple user scenarios. Experimental results have shown that, compared with other power management methods examined in this paper, AADPM achieved the highest energy saving in all cases and it demonstrated strong adaptability to network congestion.