As an emerging networking technology, LTE networks in unlicensed spectrum (named LTE-U networks) have drawn increasing attention. Due to the strict coexistence requirements from the Wi-Fi networks, quality-of-service (QoS) provisioning for delay-sensitive traffic over LTE-U networks is challenging. In this paper, assuming the LTE-U networks adopting a load based equipment (LBE) channel access mechanism supporting listen-before-talk (LBT) function, we propose a discrete-time Markov chain based approach to analyze the capacity of the LTE-U network serving delay-sensitive traffic. Specifically, we derive the maximum number of homogeneous traffic flows each with the same packet-level QoS constraints on a maximum tolerable delay and a delay violation probability. It is shown that the analytical results closely match with the simulation results, and both Wi-Fi traffic load and the QoS requirements of delay-sensitive traffic have a significant impact on the capacity of the LTE-U network.