Falling is a major cause of serious injury or even death for the elderly population. To improve the safety of elderly people, a wide range of wearable fall detection devices have been developed over recent years, such as smart watches, waistbands and other wearable fall detectors. However, most of these fall detection devices are threshold-based and have a high rate of false alarm. This paper presents a novel fuzzy logic fall detection algorithm used in smart wristbands to reduce false alarms and achieve accurate fall detection. Experiments have been conducted in our laboratory and the results show that the proposed algorithm can accurately distinguish fall events from non-fall daily activities such as walking, jumping, clapping, and so forth. It shows good potential for commercial applications.