Listen-Before-Talk (LBT) has been adopted by LTE to access unlicensed spectrum. Related contributions deal with the misalignment of LTE and WiFi slots by using reservation signal or additional channel sensing before transmissions. However, they do not consider some practical issues, such as the processing time of MAC and PHY layers due to the limit computation power of an eNodeB. Consequently, a Quality of Service (QoS) oriented scheduler for License Assisted Access (LAA) is designed in this paper with the consideration of MAC/PHY processing time. The proposed QoS oriented scheduler is divided into two sub-schedulers: Quality of Service (QoS) Scheduler (QSCH) and Resource Blocks Scheduler (RSCH). QSCH maintains the long-term QoS of each radio bearer of UEs, while RSCH deals with the real-time events, such as retransmission because of channel busy/collision on the unlicensed band. The proposed architecture of the QoS-oriented scheduler considers practical implementation issues and strikes an excellent balance between complexity and performance.