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. Besides, the buffer size bound and the jitter bound of QTNPOSS network are also presented. Moreover, by extensive numerical experiments, we discuss the influences of the Long Range Dependence (LDR) traffic property and the Weighted Fair Queuing (WFQ) weight on the proposed network performance bounds. The results show that the WFQ weight influences the bounds more greatly than the LRD property.