Mixed-criticality flows are integrated in Time-Triggered Ethernet (TTE). Offline scheduling time guarantees critical temporal determinacy of Time-Triggered (TT) flows, but it can block Rate-Constrained (RC) flows. A new scheduling algorithm named MC-iSLIP for Crossbar is proposed for scheduling mixed-criticality flows. Meanwhile, the strategy for updating pointers of inputs and outputs is designed to prevent starvation. Then the complexity of MC-iSLIP algorithm is analyzed. Finally, simulation compares TTE using output-queuing switches and input-queuing crossbar switches, which demonstrates that crossbar switches using MC-iSLIP decrease block of RC flows caused by TT flows, and decrease end-to-end delays and jitters of RC flows.