Soft exosuits are an emerging class of robots that have been shown to significantly reduce the metabolic cost of daily human movement. However, most soft exosuits are currently being studied for walking and running, and relatively minor research has been carried out on exosuits for stair climbing. Numerous exoskeletons used for stair climbing have a more rigid structure and are heavier, which may result in a greater force required by the wearer to overcome the weight from the exoskeleton when ascending stairs, which can result in metabolic costs. As a result, a reduction in rigid structures can reduce the weight of the exoskeleton and further reduce metabolic costs during stair climbing. In this paper, a waist-wearable soft exosuit was designed that assists hip flexion to aid stair climbing in older adults, in order to demonstrate the importance of choosing to assist hip flexion during stair climbing. An admittance delayed feedback control method was also proposed to use the angular information measured by the IMUs to enable the exosuit to adapt to different staircases. Metabolic experiments have shown that people who use soft exosuits have an average decrease of 6.9% in metabolism when they climb stairs than those who do not. The muscle fatigue experiments demonstrated a reduction in muscle fatigue of approximately 9.35%, 38.75% and 9.65% for the rectus femoris, lateral femoris and gastrocnemius muscles, respectively, when compared to cases without the soft exosuit. The results show that assisted hip flexion during stair climbing is a reasonable approach to effectively reduce metabolic consumption and muscle fatigue.