Network performance bounds, including the maximal End-To-End (E2E) delay, the maximal jitter and the maximal buffer backlog amount, are very important for network QoS control, buffer management and network optimization. QoS-enhanced To Next-hop POrt Sequence Switch (QTNPOSS) is a recently proposed transmission scheme to achieve scalable fast forwarding for multimedia applications. However, the existing E2E delay bound of QTNPOSS network is not tight. To this end, this paper presents a lower E2E delay bound for QTNPOSS networks by using the network calculus theory, where the inherent properties (e.g. packet length and peak rate) of the flow are taken into account.