In this paper, we propose a new quality-of-service (QoS) routing protocol for mobile ad hoc network (MANET) using directional antennas. The proposed scheme offers a bandwidth-based routing protocol for QoS support in MANET using the concept of multi-path. Our MAC sub-layer adopts the CDMA-over-TDMA channel model. The on-demand QoS routing protocol calculates the end-to-end bandwidth and allocates bandwidth from the source node to the destination node. The paths are combined with multiple cross links, called shoelace, when the network bandwidth is strictly limited. Due to the property of the directional antenna, these cross links can transmit data simultaneously without any data interference. We develop a shoelace-based on-demand QoS routing protocol by identifying shoelaces in a MANET so as to construct a QoS route, which satisfied the bandwidth requirement, more easily. The shoelace-based route from the source to the destination is a route whose sub-path is constructed by shoelace structure. With the identified shoelaces, our shoelace-based scheme offers a higher success rate to construct a QoS route. Finally, simulation results demonstrate that the proposed routing protocol outperform existing QoS routing protocols in terms of success rate, throughput, and average latency.