Power management of Wi-Fi interfaces can greatly impact the battery life time of a smart device. Thus, many commercial devices utilize the Power Save Mode - Adaptive (PSM-A) mechanism for energy saving by switching wireless radio between high and low power. Tail time is introduced in PSM-A to put the radio in high power state until the time expires, allowing near future packets to arrive without much delay. However, this fixed tail time may result in a considerable amount of energy drainage under various types of traffic. This paper proposes an adaptive tail time adjustment scheme, a simple yet efficient way to save energy wastage by adaptively resizing the tail time according to prediction of data packet arrival times. The simulation results show up to 28.4% energy savings and reduces packet delivery delay compared to existing schemes.