In this paper, we present a packet scheduling algorithm for a non-real-time service, with soft QoS requirements, which allows for degrading the QoS level, e.g., typically the packet delay, whenever necessary, in mobile broadband wireless Internet access systems. This algorithm is designed to properly trade off system throughput and delay performance, which can improve the system capacity by relaxing the delay constraint with respect to the underlying soft QoS requirement. This is as opposed to most of the existing packet scheduling algorithms for non-real-time service which are simply designed to maximize the system throughput without a delay constraint. The proposed adaptive exponential scheduling algorithm intentionally introduces additional delay to some users, especially under bad channel conditions, opportunistically allowing for serving users only under good channel conditions, as long as the resulting QoS degradation is acceptable for non-real-time service users. The results from a system-level simulation demonstrate that the system capacity can be significantly increased over existing algorithms, by as much as 65%, using the adaptive exponential scheduling algorithm while satisfying the given QoS-level requirements.