Safety-critical avionics systems which become more complex and tend to integrate multiple functionalities with different levels of criticality for better cost and power efficiency are subject to certifications at various levels of rigorousness. In order to simultaneously guarantee temporal constraints at all different levels of assurance mandated by different criticalities, novel scheduling techniques are in need. In this paper, a mixed-criticality sporadic task model with multiple virtual deadlines is built and a certification-cognizant dynamic scheduling approach referred as earliest virtual-deadline first with mixed-criticality(EVDF-MC) is considered, which exploits different relative deadlines of tasks in different criticality modes. As for the corresponding schedulability analysis problem, a sufficient and efficient schedulability test is proposed on the basis of demand-bound functions derived in the mixed-criticality scenario. In addition, a modified simulated annealing(MSA)-based heuristic approach is established for virtual deadlines assignment. Experiments performing simulations with randomly generated tasks indicate that the proposed approach is computationally efficient and competes well against the existing approaches. Safety-critical avionics systems which become more complex and tend to integrate multiple functionalities with different levels of criticality for better cost and power efficiency are subject to certifications at various levels of rigorousness. In order to simultaneously guarantee temporal constraints at all different levels of assurance mandated by different criticalities, novel scheduling techniques are in need. In this paper, a mixed-criticality sporadic task model with multiple virtual deadlines is built and a certification-cognizant dynamic scheduling approach referred as earliest virtual-deadline first with mixed-criticality (EVDF- MC) is considered, which exploits different relative deadlines of tasks in different criticality modes. As for the corresponding schedulability analysis problem, a sufficient and efficient schedulability test is proposed on the basis of demand-bound functions derived in the mixed-criticality scenario. In addition, a modified simulated annealing (MSA) -base Experiments performing simulations with randomly generated tasks indicate that the proposed approach is computationally efficient and competes well against the existing approaches.